Wave Model WAM Research Articles

Tide and surge dynamics along the Iberian Atlantic coast

The eastern Atlantic barotropic dynamics (in a region spanning from 20° N to 48° N and 34° W to 0°) are studied through numerical modelling and in situ measurements. The main source of data is the tidal gauge network REDMAR, managed by Clima Marítimo (Puertos del Estado). The numerical model employed is the HAMSOM, developed both by the Institut für Meereskunde (Hamburg University) and Clima Marítimo. In this paper, tidal and storm surge dynamics are studied for the region, focusing particularly on the nonlinear transfer of energy between the different forcings. The results of tidal simulations show good agreement between semidiurnal harmonic components and the values obtained from the tidal gauges (both coastal and pelagic) and current metres. The nonlinear transfers of energy from semidiurnal to higher order harmonics, such as M4 and M6, were mapped. Those transfers were found to be important in only two areas: The French continental shelf in the Bay of Biscay and the widest part of the African shelf, south of Cabo Bojador. The modelled diurnal constituents show larger relative differences with measurements than semidiurnal harmonics, especially in data concerning the phase. A method to isolate the nonlinear transfers of energy between tidal and atmospheric forcing during a storm surge was developed. These transfers were found to be significant in the same areas where tidal nonlinear activity was present. The effect of short period wind generated waves on sea surface elevation was also investigated. The magnitude of the spatial derivatives of radiation stress was compared with wind-induced stress. As a result of this comparison, we found the inclusion of a forcing term that depends on radiation stress in ocean model simulations at this scale and resolution to be not essential. The effect of computing wind-induced stresses, with a formulation that explicitly depends on sea state, was also explored by means of a coupled run of the HAMSOM and the spectral wave model WAM for a storm surge event in the Spanish coast. This formulation was not found to be an improvement over a classical parameterisation which only depends on wind fields.

Statistical properties of global significant wave heights and their use for validation

Global data sets of significant wave height (Hs) from altimeter measurements and from the wave model WAM are analyzed statistically to assess the quality of the data. Hs derived from the altimeters aboard Seasat (1978), Geosat (1988), ERS‐1 (1993, 1994), and TOPEX (1993, 1994) and from WAM (1988, 1993) and, in addition, from in situ data of Ocean Weather Station M in the North Atlantic are used. First, collocated data sets are compared through linear regression and principal component analysis. From this, a good agreement between Hs of the ERS‐1 altimeter (1993) and the WAM model is inferred. Second, the Hs frequency distributions are described by the first four moments. Using the first four moments of linear order statistics, the lognormal and the general extreme value distribution function are found to approximate distributions of Hs best. Hs from Seasat and ERS‐1 (1993) deviate from these empirical distribution functions, manifesting weaknesses in the data. Although Hs from ERS‐1 have weaknesses, their assimilation into WAM has a positive impact. The assessment of the quality of this existing Hs data provides a prerequisite for the coming assimilation schemes using wave data from synthetic aperture radars and also for climate research studies.

Statistical comparison of global significant wave heights from Topex and ERS-1 altimeter and from operational wave model WAM

Global data sets of significant wave height ( H s ) from radar altimeters aboard the satellites ERS-1 and Topex and from the wave model WAM are compared for 1993. The bivariate distributions from the collocation of the data are displayed in scatter diagrams. The statistical properties of bivariate distributions, where both data sets contain random errors, are best derived from principal component analysis (PCA). From this, a good agreement between H s of the ERS-1 altimeter and the WAM model is inferred. The assimilation of H s from ERS-1 altimeter into WAM is seen to have two effects. Firstly, the rms deviation between these data sets is reduced significantly. Hence the bivariate distribution narrows considerably. Secondly, as the high sea states from ERS-1 altimeter are seen to be low-biased compared to WAM before assimilation, the high sea states of WAM are reduced. This results in a rotation of the principal axes toward the right direction. The positive impact from the assimilation is proven by the significant reduction of the rms deviation between H s from WAM and the independent H s from Topex. The rotation of the distribution, however, appears to overshoot the mark.

A summary of the VIERS-1 scatterometer model

The VIERS-1 (Verification and Interpretation ERS-1) project has resulted in a new algorithm for the interpretation of the wind scatterometer, based on a physical model of air/sea/radar interaction in which the radar backscatter is calculated from wind and wave conditions. The model is inverted to obtain the wind from the radar backscatter. For operational purposes the model was coupled to the WAM wave model, which provides first-guess wave information. The performance of VIERS-1 has been compared with that of CMOD4, the algorithm presently in operational use, which is mainly based on statistical fitting. Using operational data it has been found that the results of VIERS-1 were comparable with those of CMOD4, with VIERS-1 outperforming CMOD4 slightly at both high and low wind speeds, but with CMOD4 providing a somewhat closer fit in backscatter space.

Shallow water wave modelling with nonlinear dissipation

In this paper a new shallow water wave model is described which uses nonlinear dissipation derived from turbulent diffusion as damping mechanism. The source functions of the model are presented in detail. Analytical results of the dynamical equation for simple cases illustrate basic features of the model. Academic test runs in deep and shallow water are performed. The designed cases are identical to the ones used in previous wave model intercomparison studies and thus allow comparison with other wave models. Results of a hindcast of a North Sea storm event illustrate the model behaviour in nonuniform real shallow water systems. In this case we can compare with field data and with the community wave model WAM cy. 4, which has been run parallel to our model. Our study shows that the concept of wave modelling with nonlinear dissipation is consistent with common knowledge of wave evolution in oceanic and shelf sea applications.

Introduction to nonlinear science

A Fourier series solution is presented for the time-dependent wave-modified Ekman current resulting from the Stokes drift, wind input and wave dissipation for the vertical eddy viscosity formulated by the K-Profile Parameterization scheme. An exact steady solution can be concluded as a special example. The parameters involved in the solution can be determined by the two-dimensional surface wave spectrum, wind vector, the Coriolis parameter and the densities of air and water. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with those when wave is absent or includes only the effect of the Stokes drift by using the extended Donelan and Pierson (1987) spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. The exact solutions are also compared with well-known published observational data of the Ekman layer. It is shown that the solution presented is a reasonable analytic current model with the right dependence on wind, wave and Coriolis parameter for unstratified Ekman layer.

Assimilation of wave spectra from pitch‐and‐roll buoys in a North Sea wave model

A technique for the assimilation of spectral wave observations in wave models is presented and tested. The method uses the concept of spectral partitioning to project the entire wave spectrum onto a few essential mean parameters. Model and observed partition parameters are assimilated using an optimal interpolation (OI) technique. After data reduction, obtained by the partitioning, the cost of the assimilation is negligible compared to the cost of the model run itself. Therefore the optimal interpolation of partitions (OI‐P) method is a very attractive assimilation technique for operational wave forecasting. The paper focuses on the assimilation of pitch‐and‐roll buoy spectra in a North Sea version of the WAM wave model. Treatment of the (non‐fully two‐dimensional) buoy spectra is discussed. Appropriate choices for the OI weight functions are made. The problem of correlating wave partitions in different spectra is addressed, which is essential for obtaining a robust and efficient system. In order to assess the influence of spectral wave observations on the analysis of the sea state, the method is compared to a second scheme, optimal interpolation of integral parameters (OI‐I), which can only be used to assimilate observations of significant wave height and mean wave period. First, tests with synthetic data are described, which illustrate advantages of the partitioning method over the OI‐I scheme. Also, the inherent limitations of OI are shown in both methods. Experiments with buoy observations for actual North Sea conditions show the benefits of the system, especially when several wave systems are present at the same time.

Modification of the Physics and Numerics in a Third-Generation Ocean Wave Model

Abstract The ocean wave model WAM was recently upgraded to improve the coupling between the sea state and the air flow and, in particular, enhance the growth of young wind sea over that of old wind sea. Prior to this change, numerous validations of the original wind input physics by the wave modeling community had shown a consistent underprediction of wave heights in the Southern Hemisphere. Preliminary tests of the upgraded version indicated that the change in physics improved wave height predictions but did not completely eliminate the bias. To specifically test the upgraded version, a one-month hindcast study for the Australian region was conducted using both the improved and the original physics. The hindcast significant wave heights were compared against observations from three locations wound the Australian coast and were found to he overpredicted by the upgraded physics and underpredicted by the original physics. A series of experiments were then made that indicated the upgraded physics were sensit...

Assimilation of wave data into the wave model WAM using an impulse response function method

A new method for the assimilation of wave data into a third‐generation wave model is presented. Deviations between observed and modeled wave spectra are used to derive corrections of the wind field which drives the wave model. The wave field can then be subsequently corrected by a new integration of the wave model with the improved wind field. A basic difficulty of such dynamically consistent wave data assimilations schemes which correct both wind and wave data is the nonsynchronous and nonlocal nature of the wind field corrections: errors observed in the wave spectrum at a given measurement time and location can be produced by errors in the wind field at much earlier times and far distant locations. Formally, these problems can be rigorously resolved by the adjoint modeling method. However, in practice, the adjoint technique requires an order of magnitude more computer time than the integration of the wave model itself. Here an alternative method is developed. The linearized wave model equation which relates small wind to wave spectrum changes is inverted. The central assumption of the inversion is that the wind impact functions representing the impulse response (Green's) function of the wave evolution can be approximated by a δ‐function. Physically, this implies that the wind field perturbations responsible for observed perturbations in the wave spectrum can be regarded as strongly localized in space and time for any given component of the spectrum. To obtain stable estimates, the corrections for different wave components are averaged over wavenumber clusters representing different wave systems. For cases in which the linear approximation is inadequate, the method can be applied iteratively. Tests of the concept and application of the method for a number of synthetic wind field cases are encouraging.

Measurements of the evolution of ocean wave spectra due to bottom friction

Data from a field experiment in which seven wave measurement instruments were placed in a linear transect across the Great Australian Bight are analyzed to determine the spectral decay which can be attributed to bottom friction. Since other processes such as atmospheric input, nonlinear interactions, “whitecap” dissipation, refraction, and shoaling will also be active, the spectral wave model WAM is used as an analysis tool, explicitly taking these additional processes into account in the analysis. The data show marked spectral decay across the shelf. Analysis reveals that the bottom friction coefficient Cƒ is not constant as often assumed in operational wave models. The bottom friction coefficient varies approximately inversely with the wave‐induced bed velocity, consistent with the predictions of previous laboratory data and eddy viscosity models. It is possible that percolation may also be important in the region, but the available data do not allow the relative contributions of bottom friction and percolation to be determined.

Wave data assimilation in the WAM wave model

Abstract Using the adjoint technique, wave height data have been assimilated into the third generation ocean wave model WAM, which runs operationally at ECMWF. WAM describes the evolution of a two-dimensional wave spectrum and it is driven by surface winds. WAM considers three source functions: wind input, dissipation by white capping and non-linear wave-wave interactions between the different components of the spectrum. The wind input term is taken from the theory of Janssen (1991). According to this theory, the drag coefficient depends not only on the wind speed but also on the wave spectrum through the wave stress. Up to now, a one-gridpoint version of the adjoint of the WAM has been constructed and tested. The assimilation scheme optimizes the driving wind sequence. The potential benefit of the scheme is investigated by performing some idealized experiments.

A sequential assimilation scheme applied to global wave analysis and prediction

Abstract This paper examines the results of the assimilation of satellite Significant Wave Height (SWH) observations in a global wave prediction model. The model used is the third generation wave model WAM. The assimilation is carried out using a sequential (single time level) scheme. Each assimilation step is split into two parts. The analysed SWH field is built by Optimal Interpolation, and the analysed spectrum is successively derived from it and from the first guess spectrum. The period used in the study is February 1992, and the altimeter data have been provided by the ERS-1 satellite. The results show positive effects of the assimilation on both wave analysis and forecast.

Variational Wave Data Assimilation in a Third-Generation Wave Model

Abstract The adjoint of the wave model WAM, which runs operationally performing global wave forecast at the European Centre for Medium-Range Weather Forecasts, has been constructed. In this model, the nonlinear interactions are described by the discrete interaction approximation of Hasselmann et al., and the wind input and the dissipation are consistent with the theory of Janssen. The drag coefficient depends not only on the wind speed, but also on the wave-induced stress, reflecting in this way the dependence of winds on waves. The adjoint scheme constitutes a new (the first variational) method to assimilate arbitrary wave data into the WAM. Up to now, this had been done using an optimal interpolation technique (sequential method), and only for wave heights. The new assimilation scheme has been tested with a one-gridpoint version of the WAM. Assimilating only wave data-significant wave height and mean wave direction—is sufficient to reconstruct all wind fields, significant wave height, and two-dimensiona...

Global validation of the wave model WAM over a one‐year period using Geosat wave height data

The high quality of wave fields simulated by the third‐generation wave model WAM has already been demonstrated in various validation studies using in situ measurements as well as data from satellites as reference. However, owing to limitations of the reference data sets, the previous studies concentrated on relatively small regions or short time periods only, for which adequate measurements were available. In this paper the first global verification of the WAM model over a full 1‐year period is presented. The significant wave heights hindcast for 1988 by the WAM model as implemented at the European Centre for Medium Range Weather Forecasts are compared with measurements obtained by the Geosat radar altimeter. The wave heights from WAM and Geosat show good agreement in general. However, significant regional and seasonal differences are found. The underestimation of WAM wave heights in the southern hemisphere, which was already known from a validation study for the Seasat period, shows significant seasonal variations. The hindcast wave heights are underestimated by about 20% in large parts of the southern hemisphere and the tropical region during May‐;September. For the rest of the time, the agreement with Geosat data is fairly good. Together with the fact that also the rms variability of wave heights in the tropical region is clearly underestimated by WAM, this can possibly be attributed to simplifications like the neglect of atmospheric stratification effects when converting wind speeds to the wind stress fields driving WAM. Furthermore, the intercomparison indicates that low wave heights below ∼ 1.5 m are generally overestimated by WAM. As it is planned to use altimeter wave heights for updating wave models in future data assimilation systems, it is quite important to have efficient quality control criteria for these data. We show that some additional Geosat parameters, e.g., the off‐nadir angle of the altimeter, can be useful quality parameters. The difference between the Geosat and WAM wave heights shows a clear dependence on the additional parameters in some cases, which must be related to quality problems of the Geosat data. Some new criteria for the rejection of incorrect Geosat data points are obtained.

Boundary-Layer Model Results for Wind-Sea Growth

A numerical model of the boundary layer of the atmosphere above a gravity surface wave is reviewed. The model results are used to obtain an expression for the wind input, the wave growth due to the wind. This is done for wave components that propagate at an arbitrary angle to the wind. Like other purely theoretical expressions for the wind input, the wind input from the boundary-layer model is much smaller than the wind input inferred from field experiments. To study the growth of wind sea, the wind input of the third-generation wave model WAM is replaced by the wind input from the boundary-layer model. The original WAM used a wind input that was inferred from field experiments. For the wave-wave interactions the discrete-interaction approximation is used, while the dissipation is tuned to get an appropriate saturation sea state. The balance between wind input, dissipation, and wave-wave interactions in the energy-containing range of the wave spectrum in this version of the WAM is very different from the balance between these terms in the original version of the WAM. Nevertheless, in both versions of the WAM the development of the wave spectrum of growing wind sea is in agreement with experimental data. It is concluded that a wave model based on the wave boundary-layer wind-input term is quite capable of reproducing the observed growth of wind sea.

Assimilation of altimeter data in a global third‐generation wave model

We investigated the effect of the assimilation of altimeter satellite data in the third‐generation ocean wave model WAM. We used a sequential method, where analyzed significant wave height fields are created by optimum interpolation, and the analyzed values are then used to construct the analyzed wave spectrum. The method provides also an estimate of the surface stress showing the possibility of using the analysis of the wave spectrum to derive an analyzed surface stress field. In a first set of numerical experiments, the data, provided by the Seasat altimeter, have been assimilated in the WAM model for 1½ days. The comparison between model results and satellite data during the continuation of the run shows a positive and persistent impact of the assimilation. In a second set of numerical experiments, Geosat altimeter data were assimilated for 10 days and the resulting analysis was compared with buoy data. Although the assimilation improves the model results, it is not capable of compensating the differences between model and buoys. Some failures are clearly derived from the absence in the satellite data of the high‐wave events that were reported by the buoys. Other failures may be the consequence of an excessive swell attenuation in the WAM model, which compromises the effect of a previous correction. In fact, the comparison of WAM model results with altimeter data suggests that there is a tendency of the model to overevaluate initially the wind sea, and successively to overestimate the decay of the wave energy, when the waves leave the area of the storm.

Validation and assimilation of Seasat altimeter wave heights using the WAM wave model

The mutual consistency of the Seasat global data sets of scatterometer winds and altimeter wave heights is investigated for the complete Seasat period using the third‐generation wave model WAM. The wave model was driven by surface (1000 hPa) wind and surface stress fields constructed by the Goddard Laboratory for Atmospheres (GLA) by assimilation of the scatterometer winds in an atmospheric model. For the 10‐day period September 7–17 the intercomparison was extended to two further scatterometer wind fields: a 1000‐hPa assimilated wind field from the European Centre for Medium‐Range Weather Forecasts and a subjectively analyzed 19.5‐m‐height surface wind field from the Jet Propulsion Laboratory. On the global average, the modeled and observed wave heights agree reasonably well. Regional differences, however, can be large and sometimes exceed 40%. The errors are attributed mainly to deficiencies in the forcing wind fields. Low wind speeds are found to be overestimated and high wind speeds underestimated by the Seasat scatterometer algorithm. The friction velocities of the GLA model are found to be significantly underestimated in the high‐wind belt of the southern hemisphere. The analysis demonstrates the diagnostic advantages of applying a wave model for the quality assessment of satellite wind and wave data. A preliminary wave data assimilation scheme is presented in which the wave field is updated without changing the forcing wind field. A considerable improvement of the computed wave field is achieved, particularly in regions in which the wave energy is dominated by swell. However, a more general assimilation scheme including modifications of the wind field is needed to upgrade wind sea forecasts.

Shallow water application of the third‐generation WAM wave model

We present the results of detailed tests of the third‐generation WAM wave model. The tests are carried out under well‐known conditions, and they are chosen so as to check different aspects of the model. The test area is the Adriatic Sea, east of Italy, which is very shallow in its northern part. As expected from the basic physical approach of WAM to the problem, the results show the model's capability of responding equally well to different meteorological situations. Some discrepancies present at short nondimensional fetch and in shallow water are addressed with different formulations for breaking and bottom friction.

Numerical Modelling Of Three-dimensional Non-Cohesive Sediment Transport In Java Sea

In the framework of an integrated research project on prediction of beach and sea floor topography changes in Java Sea, the development of a three-dimensional non-cohesive sediment transport model to predict suspended sediment fluxes has been carried out by solving the advection-diffusion equation. The velocity fields were calculated by using a three-dimensional hydrodynamic model of tideand wind-driven circulation incorporating the influence of wind waves generated at the sea surface. The third generation wave model WAM (WAMDI ) was used to calculate the wave parameters and the wave dependence of the drag coefficient. To represent the monsoon wind fields which play an important role in generating the waves and water circulation in the region, ECMWF's one-year hindcasted data of six hourly-wind fields at 10 m above the sea surface were used in the simulation. The simulation results show that both for the typical westand east-monsoon the largest values of the suspended sediment concentration can be observed around central part of the Java Sea, where the velocities are largest. One-year computation of the bed level changes in the region produces erosion and deposition in the range 0 to 1.5 cm. Due to the most of the sea floor of the Java Sea being covered by mud (Emery et a//), the model will be extended to predict cohesive sediment transport. These kinds of studies are currently in progress as an extension of this research program. Transactions on the Built Environment vol 40 © 1999 WIT Press, www.witpress.com, ISSN 1743-3509