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.

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

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The sections in this article are


1
Radiometers

2
Radar Scattering

3
Radar Scatterometers

4
Radar Altimeters

5
Ground-Penetrating Radars

6
Imaging Radars

7
Real-Aperture Radars

8
Synthetic-Aperture Radars

Microwave Remote Sensing

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

: The data for the spectra of fully developed seas obtained for wind speeds from 20 to 40 knots as measured by anemometers on two weather ships are used to test the similarity hypothesis and the idea that, when plotted in a certain dimensionless way, the power spectra for all fully developed seas should be of the same shape as proposed by Kitaigorodskii (1961). Over the important range of frequencies that define the total variance of the spectrum within a few percent, the transformed plots yield a non-dimensional spectral form that is nearly the same over this entire range of wind speeds within the present accuracies of the data. However, since slight variations of the wind speed have large effects on the location of this non-dimensional spectral form, inaccuracies in the determination of the wind speed at sea allow for some latitude in the final choice of the form of the spectrum. Also since the winds used to obtain the non-dimensional form were measured at a height greater than ten meters, the problem of relating the spectral form to a standard anemometer height arises. The variability introduced by this factor needs to be considered. The results, when errors in the wind speed, the sampling variability of the data, and the anemometer heights are considered, suggest a spectral form that is a compromise between the various proposed spectra and that has features similar to many of them.

A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii

To provide theoretical basis for the connection between observed radar scattering and wind-generated waves, a model for the response of surface waves in the gravity-capillary equilibrium region of the spectrum is proposed on the basis of a local (in wavenumber) balance between wind input and dissipation. The wind input function was constructed on the basis of laboratory observations of short-wave growth, while the dissipation function was developed from ideas of viscous dissipation and wave breaking in response to local accelerations and modified by kinematic effects of phase and group velocity differences. The model was exercised at L, C, X, and Ka bands to demonstrate the differences in wind speed and water temperature sensitivity.

Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

A description is given of the algorithm used to convert Seasat-A satellite microwave scatterometer measurements of ocean normalized radar cross section to the neutral stability vector wind at 19.5 m height, as well as to compare these winds with high-quality surface observations. The wind vector algorithm used an empirical normalized radar cross section model function to describe the ocean normalized radar cross section's dependence on the 19.5-m neutral stability wind vector. In addition, two model functions were evaluated by means of an independent set of in situ surface wind observations from the Joint Air Sea Interaction experiment (JASIN). Better results were produced by these comparisons than the stipulated Seasat wind speed and direction accuracy specifications of + or - 2 m/sec and + or - 20 deg, respectively, over the 0-16 m/sec range of winds observed during JASIN.

The Seasat-A satellite scatterometer - The geophysical evaluation of remotely sensed wind vectors over the ocean

The Navier-Stokes equations for incompressible flow in their Lagrangian form are taken as a starting point A perturbation technique is then used to obtain first- and second-order sets of equations, and the general procedure for solving the equations to any order is given The first-order equations yield interesting two- and three-dimensional motions that have some of the properties of ‘stirring’ ‘eddies’ and ‘turbulence’; it is suggested that various problems in turbulent motion might possibly be re-examined by means of these equations

Perturbation analysis of the Navier‐Stokes equations in Lagrangian form with selected linear solutions

Mesoscale and microscale features of the turbulent winds over the ocean are related to the synoptic scale winds in terms of published spectral forms for the microscale, a mesoscale valley and published values of U*, VAR u', VAR v' and z/L, as defined in the text and as obtained for moderate to gale force winds. The frequencies involved correspond to periods longer than 1 hour and extend to the microscale, which starts at a period near 2 minutes, or so, and continues to the Kolmogorov inertial range. Nondimensional spectra that span both the mesoscale and the microscale are derived as a function of u, f(= n z/u) and z/L, where z is 10 meters, L is the Monin Obukov stability length and u is evaluated at 10 meters. For the same u, different values of z/L produce a range of values of u which in turn result in variations of the eddy structure of the mesoscale and microscale spectra. Both conventional anemometer averages and remotely sensed winds contain a random component of the mesoscale wind in their values. These components are differnces and not errors when winds are compared, and quantitative values for these differences are given. Ways to improve the measurement of the synoptic scale wind by transient ships, data buoys and scatterometers on future spacecraft are described. These ways are loner averaging times for ships and data buoys, depending on the synoptic conditions, and pooling spacecraft to form super observations. Design considerations for future remote sensing systems are given.

/pdf/the-measurement-of-the-synoptic-scale-wind-over-the-ocean-15vm3auigz.pdf

Willard J. Pierson

Papers

A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii

Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

The Seasat-A satellite scatterometer - The geophysical evaluation of remotely sensed wind vectors over the ocean

Perturbation analysis of the Navier‐Stokes equations in Lagrangian form with selected linear solutions

The measurement of the synoptic scale wind over the ocean