Gerbrand J. Komen

New evidence for a relation between wind stress and wave age from measurements during ASGAMAGE

Data from the 1996 ASGAMAGE experiment, performed in the southern North Sea at research platform Meetpost Noordwijk (MPN), are analysed for the parameters affecting the momentum flux. The stress turns out to be quadratically related to the 10-m wind speed and linearly to the wind speed at a wavelength related level. The Charnock parameter (dimensionless roughness length) shows a pronounced correlation with wave age. This implies, due to a coupling between wave age and the steepness of the waves, a connection between the stress and the steepness. We find that our North Sea results are consistent withopen ocean observations. For a given wind speed the mean stress at MPN turns out to be higher because the wave age there is in general lower. We define and give an expression for a drag coefficient at a wavelength related level that can be calculated straightforwardly from the wave age and then reduced to a standard level.

On phase velocity and growth rate of wind-induced gravity-capillary waves

The generation and growth of gravity-capillary waves by wind are considered using linear instability theory to describe the process. The growth rate of the initial wavelets, the first waves to be generated by wind, is found to be proportional to the cube of the friction velocity in air. The effect of changes in the shape of the profiles of wind and wind-induced current is also considered; the growth rate is found to be very sensitive to the shape of the wind profile while the influence of changes in the current profile is much smaller. The values of the current and the current shear at the interface are much more important for determining the phase velocity correctly than the shape of either the wind or the current profile.

Interannual variability in the Southern Ocean from an ocean model forced by European Centre for Medium-Range Weather Forecasts reanalysis fluxes

Anomaly patterns in the Southern Ocean in response to variability in the atmospheric forcing are investigated. To this end we forced the Hamburg large-scale geostrophic ocean general circulation model with surface fluxes from the European Centre for Medium-Range Weather Forecasts reanalysis (ERA). ERA covers the period January 1979 through February 1994. First, the atmospheric variability of sea level pressure and the associated wind stress anomalies within the ERA data set are analyzed. An Antarctic Circumpolar Wave type pattern is identified. In the ocean response, sea water temperature and salinity anomalies are found to vary with similar periods. The anomalies advect with the Antarctic Circumpolar Current. High amplitudes occur in the southeast Indian and Pacific Oceans. Sensitivity studies are made, pinning down wind stress and heat flux as the dominant factors generating these anomalies. The oceanic interannual variations are explained in terms of enhanced oceanic convection resulting from anomalous Ekman pumping and anomalous heat fluxes, both operating in a standing pattern dominated by wavenumbers 2 and 3.

Friction velocity scaling in wind wave generation

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.

Wave data assimilation with the Kalman filter

A new data assimilation method for ocean waves is presented, based on an efficient low-rank approximation to the Kalman filter. Both the extended Kalman filter and a truncated second-order filter are implemented. In order to explicitly estimate past wind corrections based on current wave measurements, the filter is extended to a fixed-lag Kalman smoother for the wind fields. The filter is tested in a number of synthetic experiments with simple geometries. Propagation experiments with errors in the boundary condition showed that the KF was able to accurately propagate forecast errors, resulting in spatially varying error correlations, which would be impossible to model with time-independent assimilation methods like OI. An explicit comparison with an OI assimilation scheme showed that the KF also is superior in estimating the sea state at some distance from the observations. In experiments with errors in the driving wind, the modeled error estimates were also in agreement with the actual forecast errors. The bias in the state estimate, which is introduced through the nonlinear dependence of the waves on the driving wind field, was largely removed by the second-order filter, even without actually assimilating data. Assimilation of wave observations resulted in an improved wave analysis and in correction of past wind fields. The accuracy of this wind correction depends strongly on the actual place and time of wave generation, which is correctly modeled by the error estimate supplied by the Kalman filter. In summary, the KF approach is shown to be a reliable assimilation scheme in these simple experiments, and has the advantage over other assimilation methods that it supplies explicit dynamical error estimates.

Effect of atmospheric stability on the growth of surface gravity waves

In this paper we study the effect of atmospheric stability on the growth of surface gravity waves. To that end we numerically solved the Taylor-Goldstein equation for wind profiles which deviate from a logarithmic form because stratification affects the turbulent momentum transport. Using Charnocks relation for the roughness height z0 of the wind profile, it is argued that the growth rate of the wave depends on the dimensionless phase velocity c/u* (where u* is the friction velocity) and a measure of the effect of atmospheric stability, namely the dimensionless Obukhov length gL/u*2, whereas it only depends weakly on gzt/u*2 (where zt is the roughness height of the temperature profile). Remarkably for a given value of u*/c, the growth rate is larger for a stable stratification (L > 0) than for an unstable one (L < 0). We explain why this is the case. If, on the other hand, one considers the growth rate as a function of c/U10 (where U10 is the windspeed at 10 m), the situation reverses for c/U10 < 1. For practical application in wave prediction models, we propose a new parameterization of the growth rate of the waves which is an improvement of the Snyder et al. (1981) proposal because the effect of stability is taken into account.

Indications for a wave dependent charnock parameter from measurements during ASGAMAGE

Eddy-correlation measurements of the wind stress and wave measurements were made during ASGAMAGE, an experiment carried out in 1996 at research platform Meetpost Noordwijk (MPN) in the southern North Sea. An analysis of the results confirms the predicted wave dependence of the Charnock parameter. As in HEXOS, an earlier experiment at the same platform, the corresponding values of the drag are higher than those found in the open ocean. We show that this is consistent with the existence of a wave-age dependent Charnock parameter and the fact that, for given wind speed, on average, wave ages are lower at MPN than in the open ocean.

The influence of atmospheric stratification on the growth of water waves

The atmospheric surface layer over sea has a density stratification which varies with moisture content and air/sea temperature difference. This influences the growth of water waves. To study the effect quantitatively, the Reynolds equations are solved numerically. For given wind speed and surface roughness, wave growth is found to be more rapid in unstably stratified conditions than in stable conditions. This is due to an increase in turbulence, primarily caused by an increase of mixing length.Under the assumption of a Charnock relation between surface roughness and friction velocity, it is found that for large inverse wave age (u*/c>0.07), the effect of stratification on wave growth is weell described by Monin-Obukhov scaling of the friction velocity. For smaller values ofu*/c, Monin-Obukhov scaling overpredicts.The effect on duration-limited wave growth is studied with the third-generation WAM surface wave model driven by 10 m winds. Effects of stratification on the significant wave height are found to be of the order of 10%. The results are comparable to those of a recent reanalysis of field measurements, although the measured stratification effect is somewhat stronger. Implementation of a stratification-dependent growth in wave models is recommended, as it can lead to small but significant improvements in wave forecasts when accurate air and sea temperatures are available.

Shallow Water Intercomparison of Wave Models — Part III

This paper describes the intercomparison and verification of results from three operational shallow water wave prediction models in their hindcasts of a severe storm period. The three models, BMO (Meteorological Office), GONO (KNMI) and HYPAS (Max-Planck-Institut) have already been compared theoretically and via idealised experiments with constant winds in Parts I and II of the SWIM project (SWIM Group, 1985). The work reported here attempts to unravel the complicated processes involved in the prediction of shallow water waves in a complex synoptic situation by running all three models in parallel with common wind fields and similar computation grids and bottom topography. The case chosen, two North Sea storms in November 1981, is fully described in SWIM (1984). Results presented here show that all models produce broadly similar results and acceptable shallow water energy levels at three verification sites, despite the differences in formulation and results shown in Parts I and II of this project.

The KNMI Operational Wave Prediction Model GONO

Routine wave forecasting for the southern North Sea is performed by the Royal Netherlands Meteorological Institute (KNMI) with the numerical wave model gono (GOlven NOordzee) (Janssen et al., 1984). This model was developed by Sanders (1976) in the early 1970s based on an idea by Haug (1968). Application of the model to the southern part of the North Sea necessitated the incorporation of shallow-water effects. These extensions have been recently reported by Sanders et al. (1980, 1981). The model has been calibrated and tested in a hindcast study of several storms (cf. Sanders et al., 1980) and it has been verified for operational purposes against wave data from several positions (cf. Bouws et al., 1980a,b). Furthermore, the shallow-water results in the gono model during the winter 1979–1980 have been compared with those of the bmo model (Golding, 1978), which is operational at the British Meteorological Office (cf. Bouws et al., 1980a,b, 1981).