This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.

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The Interaction of Ocean Waves and Wind

Turbulent fluxes have been measured in the atmospheric surface layer from a boom extending upwind from the Dutch offshore research platform Meetpost Noordwijk (MPN) during HEXMAX (Humidity Exchange over the Sea Main Experiment) in October–November, 1986. We started out to study eddy flux of water vapour, but discrepancies among simultaneous measurements made with three different anemometers led us to develop methods to correct eddy correlation measurements of wind stress for flow distortion by nearby objects. We then found excellent agreement among the corrected wind stress data sets from the three anemometers on the MPN boom and with eddy correlation measurements from a mast on a tripod. Inertial-dissipation techniques gave reliable estimates of wind stress from turbulence spectra, both at MPN and at a nearby ship. The data cover a range of wave ages and the results yield new insights into the variation of sea surface wind stress with sea state; two alternative formulas are given for the nondimensional surface roughness as a function of wave age.

Sea surface wind stress and drag coefficients: The hexos results

A prediction model for stationary, short-crested waves in shallow water with ambient currents

This paper describes development and validation of a global climatology of basic wave parameters based on the voluntary observing ship (VOS) data from the Comprehensive Ocean-Atmosphere Data Set collection. Climatology covers the period 1958–1997 and presents heights and periods for the wind sea, swell, and significant wave height (SWH) over the global ocean on 2° × 2° spatial resolution. Significant wave height has been derived from separate sea and swell estimates by taking square root of the sum of squares for the seas and swells propagating approximately in the same direction and assuming SWH to be equal to the higher of the two components in all other cases. Special algorithms of corrections were applied to minimize some biases, inherent in visual wave data. Particularly, we corrected overestimation of small seas, corrected underestimation of periods, and analyzed separation between sea and swell. Validation included estimation of random observational errors, observation of sampling errors, and comparison with the alternative wave data. Estimates of random observational errors show that for the majority of locations, observational uncertainties are within 20% of mean values, which allows us to discuss quantitatively the produced climatology. Biases associated with inadequate sampling were quantified using the data from high-resolution WAM hindcast for the period 1979–1993. The highest sampling biases are observed in the South Ocean, where wave height may be underestimated by 1–1.5 m because of poor sampling, primarily associated with a fair weather bias of ship routing and observation. Comparison to the other VOS-based products shows in general higher SWH in our climatology, especially in the midlatitudes. However, comparison with the altimeter data shows that even for well-sampled regions, high waves are still underestimated in VOS, suggesting a ubiquitous fair weather bias. Further ways of improving VOS-based wave climatologies and possible applications are discussed.

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Assessment of the reliability of wave observations from voluntary observing ships: Insights from the validation of a global wind wave climatology based on voluntary observing ship data

The ERA (European Centre for Medium-Range Weather Forecasts Reanalysis) project resulted in a homogeneous data set describing the atmosphere over a time span of 15 years, from 1979 to 1993. To validate (part of) these data against independent observations we use the ERA surface winds to drive the WAM wave model. The modeled significant wave heights are then compared with observations. From this comparison the quality of the forcing winds is assessed. The patterns of computed wave heights agree well with observed patterns, and they are of the right magnitude. This confirms the realistic nature of the ERA winds. If one looks in detail, it appears that the significant wave heights resulting from the model are systematically lower than the observed ones in areas of high winds and waves and higher in areas of low winds and waves. It is argued that underestimation at high winds speeds is most likely a resolution effect, as wind and thus wave peaks are missed by finite resolution in space and time, while overestimation at low wind speeds most likely results from internal WAM errors. It is concluded that the monthly mean ERA winds are slightly (less than 5%) too low in areas of high winds, while from this study it is not possible to draw a decisive conclusion on the quality of ERA winds at low wind speeds. At the same time, the hindcast data form a 15-year climatology of global waves. This climatology is analyzed in terms of annual cycle and trends. The largest trends in significant wave height occur in the North Atlantic with an increase of more than 12 cm/yr in January, and south of Africa where the increasing trend exceeds 7 cm/yr in July. These trends, however, are only marginally significant. Furthermore, they exhibit a large month-to-month variability, so that on a seasonal basis the trends are significant only in small parts of the ocean. In conclusion, we are unable to confirm a significant change in wave height during the ERA period.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JC03431

Fifteen years of global wave hindcasts using winds from the European Centre for Medium‐Range Weather Forecasts reanalysis: Validating the reanalyzed winds and assessing the wave climate

GONO is a numerical wave prediction model used for the preparation of forecasts as well as hind-casts. It is a hybrid model: the wind sea is described in a parametric way, but swell is treated in a spectral manner. For the wind sea there are two prognostic parameters: the zero-moment wave height and the mean direction. Pure wind-sea spectra are assumed to have a quasi-universal shape: above the spectral peak, ƒ−5 behavior is assumed; below the peak, a linear frequency dependence is taken. The directional dependence is of the cos2 θ type. Empirical relations are used to derive the full set of wind-sea parameters from the prognostic variables and the wind vector. The equations for the prognostic variables are solved on a discrete grid with the help of a simple finite-difference scheme. For the accurate propagation of swell, possibly over large distances, a ray technique is used. The full two-dimensional spectrum is reconstructed for selected grid points for which the results of the ray technique and the wind-sea calculations are combined. The model is a shallow water model because bottom dissipation effects are taken into account, but effects of refraction are disregarded. Depending on wind speed, these effects may be important in areas where the depth is less than about 100 m. The model has not been applied in regions with depths less than 15 m, therefore extreme shallow water effects are not considered. The behavior of the model was studied in quite some detail during the recent Sea Wave Modeling Project (SWAMP) in a few idealized situations. Knowledge of the model behavior in more realistic situations stems from its routine operational application. Runs are made four times a day on a grid covering the North Sea and the Norwegian Sea, and the results are monitored continuously. Presently, we have a data base containing about four years of observations and model predictions. From this data base we discuss a few interesting storms, and we present a statistical analysis of all of the available material. As part of this analysis we consider the effect of the quality of the input winds on the model performance.

An operational coupled hybrid wave prediction model

This note is devoted to the problem of the appropriate scaling of parameters relevant for sea waves, such as wave height, peak frequency, duration, and fetch. In the past, the growth of sea waves has often been analysed in terms of the wind velocity at a fixed height, despite the fact that many authors have stressed the importance of scaling with the friction velocity. This problem would be immaterial if the ratio between the friction velocity and the wind speed at a fixed height were a constant. There is, however, ample evidence that this ratio increases with wind speed (Smith and Banke, 1975; Smith, 1980), in agreement with dimensional considerations by Charnock (1955) on the friction height. As a result, the scaling problem is an important one. In this note we conjecture that the correct procedure is to scale wave parameters with friction velocity, and we discuss experimental evidence for the correctness of this conjecture. Comparing two independent datasets (‘JONSWAP’ and ‘KNMI’), we find some evidence supporting our ideas. Further confirmation remains desirable, however, and suggestions are made as to how this might be obtained.

Friction velocity scaling in wind wave generation

We have investigated the effect of bottom friction on the evolution of wind sea for a constant wind speed. This was done by integrating the transport equation for the energy density over frequency and direction, assuming the Kruseman spectrum for wind sea. The wind input term was derived from empirical data whereas the bottom friction term was obtained from an average (over frequency and direction) of the linearized JONSWAP dissipation form. For a flat bottom and infinite fetch we obtained the following results: 

(i)

For infinite duration the results for the nondimensional wave height and peak period versus nondimensional depth are in good agreement with a number of measurements.




(ii)

The saturation level of the wave energy is rather insensitive for variations in the dissipation coefficient.






Form this we may conclude that our results apply for different types of bottoms, thereby explaining why at sea approximately the same saturation level for wind sea is found for different bottoms.

Willem J. P. De Voogt

Papers

An operational coupled hybrid wave prediction model

Friction velocity scaling in wind wave generation

On the Effect of Bottom Friction on Wind Sea