Hendrik L. Tolman

A Third-Generation Model for Wind Waves on Slowly Varying, Unsteady, and Inhomogeneous Depths and Currents

Abstract A full discrete spectral model for propagation generation and dissipation of wind waves for arbitrary depth, current and wind fields is presented (WAVEWATCH). This model incorporates all relevant wave-current interaction mechanisms including changes of absolute frequencies due to unsteadiness of depth and currents. The model furthermore explicitly accounts for growth and decay of wave energy and for nonlinear resonant wave-wave interactions. The numerical schemes for propagation are basically second-order accurate. Effect of refraction and frequency shifts (due to unsteadiness of depth and current) are calculated on a fixed grid, also using second-order schemes. This paper focuses on the governing equations and the numerical algorithms. Furthermore some results for academic and realistic cases are presented to illustrate some features and merits of the model.

Source Terms in a Third-Generation Wind Wave Model

Abstract A new third-generation ocean wind wave model is presented. This model is based on previously developed input and nonlinear interaction source terms and a new dissipation source term. It is argued that the dissipation source term has to be modeled using two explicit constituents. A low-frequency dissipation term analogous to wave energy loss due to oceanic turbulence is therefore augmented with a diagnostic high-frequency dissipation term. The dissipation is tuned for the model to represent idealized fetch-limited growth behavior. The new model results in excellent growth behavior from extremely short fetches up to full development. For intermediate to long fetches results are similar to those of WAM, but for extremely short fetches the present model presents a significant improvement (although the poor behavior of WAM appears to be related to correctable numerical constraints). The new model furthermore gives smoother results and appears less sensitive to numerical errors. Finally, limitations of...

Development and implementation of wind-generated ocean surface wave models at NCEP

Abstract A brief historical overview of numerical wind wave forecast modeling efforts at the National Centers for Environmental Prediction (NCEP) is presented, followed by an in-depth discussion of the new operational National Oceanic and Atmospheric Administration (NOAA) “WAVEWATCH III” (NWW3) wave forecast system. This discussion mainly focuses on a parallel comparison of the new NWW3 system with the previously operational Wave Model (WAM) system, using extensive buoy and European Remote Sensing Satellite-2 (ERS-2) altimeter data. The new system is shown to describe the variability of the wave height more realistically, with similar or smaller random errors and generally better correlation coefficients and regression slopes than WAM. NWW3 outperforms WAM in the Tropics and in the Southern Hemisphere, and they both show fairly similar behavior at northern high latitudes. Dissemination of NWW3 products, and plans for its further development, are briefly discussed.

Treatment of unresolved islands and ice in wind wave models

Abstract In ocean wave prediction models, unresolved islands are a major source of (local) errors. This paper presents a method based on a technique used in the SWAN model to deal with such islands. The method is tested in the operational global WAVEWATCH III model of the National Centers for Environmental Prediction with a one year hindcast, and the results show a local but dramatic impact on model errors. An added benefit of this methodology is the possibility to model the effects of polar ice coverage on waves continuously. A simple model to continuously model ice coverage is suggested. This new ice model shows mixed results in the tests.

Numerical Simulation of Sea Surface Directional Wave Spectra under Hurricane Wind Forcing

Numerical simulation of sea surface directional wave spectra under hurricane wind forcing was carried out using a high-resolution wave model. The simulation was run for four days as Hurricane Bonnie (1998) approached the U.S. East Coast. The results are compared with buoy observations and NASA Scanning Radar Altimeter (SRA) data, which were obtained on 24 August 1998 in the open ocean and on 26 August when the storm was approaching the shore. The simulated significant wave height in the open ocean reached 14 m, agreeing well with the SRA and buoy observations. It gradually decreased as the hurricane approached the shore. In the open ocean, the dominant wavelength and wave direction in all four quadrants relative to the storm center were simulated very accurately. For the landfall case, however, the simulated dominant wavelength displays noticeable overestimation because the wave model cannot properly simulate shoaling processes. Direct comparison of the model and SRA directional spectra in all four quadrants of the hurricane shows excellent agreement in general. In some cases, the model produces smoother spectra with narrower directional spreading than do the observations. The spatial characteristics of the spectra depend on the relative position from the hurricane center, the hurricane translation speed, and bathymetry. Attempts are made to provide simple explanations for the misalignment between local wind and wave directions and for the effect of hurricane translation speed on wave spectra.

Effects of Numerics on the Physics in a Third-Generation Wind-Wave Model

Abstract Numerical errors in third-generation ocean wave models can result in a misinterpretation of the physics in the model. Using idealized situations, it is shown that numerical errors significantly influence the initial growth, the response of wave fields to turning winds, the scaling behavior of model results with wind speed, and the propagation of swell. Furthermore, the numerics may influence the dynamic interaction between wind sea and swell. Surprisingly, fetch-limited model behavior is hardly influenced by numerical errors in wave propagation. Simple modifications of the numerics are presented to reduce or eliminate such errors. The impact of numerical improvements for realistic conditions is illustrated by performing hindcasts for the Atlantic basin and for a smaller region off the east coast of the United States.

Alleviating the Garden Sprinkler Effect in wind wave models

Abstract In ocean wave models, swell propagation at coarse spectral resolution leads to the disintegration of continuous swell fields into discrete swell fields. This process is known as the Garden Sprinkler Effect (GSE). An existing solution to the GSE consists of adding a diffusion tensor to the propagation equation. Although this diffusion method has been proven successful, it is prohibitively expensive for models with high spatial resolution. Two alternatives are presented here. The first is an averaging method. It shares characteristics with the diffusion method, but is much cheaper for high resolution models. The second method consists of adding divergence to the advection field. This divergence method is shown to be accurate for idealized conditions, and requires less tuning, but is still too expensive to replace the other methods in practical conditions. It is therefore suggested to replace the diffusion method with an averaging method in operational models, and to investigate the divergence method further.

A neural network technique to improve computational efficiency of numerical oceanic models

A new generic approach to improve computational efficiency of certain processes in numerical environmental models is formulated. This approach is based on the application of neural network (NN) techniques. It can be used to accelerate the calculations and improve the accuracy of the parameterizations of several types of physical processes which generally require computations involving complex mathematical expressions, including differential and integral equations, rules, restrictions and highly nonlinear empirical relations based on physical or statistical models. It is shown that, from a mathematical point of view, such parameterizations can usually be considered as continuous mappings (continuous dependencies between two vectors). It is also shown that NNs are a generic tool for fast and accurate approximation of continuous mappings and, therefore, can be used to replace primary parameterization algorithms. In addition to fast and accurate approximation of the primary parameterization, NN also provides the entire Jacobian for very little computation cost. Three successful particular applications of the NN approach are presented here: (1) a NN approximation of the UNESCO equation of state of the seawater (density of the seawater); (2) an inversion of this equation (salinity of the seawater); and (3) a NN approximation for the nonlinear wave–wave interaction. The first application has been implemented in the National Centers for Environmental Prediction multi-scale oceanic forecast system, and the second one is being developed for wind wave models. The NN approach introduced in this paper can provide numerically efficient solutions to a wide range of problems in environmental numerical models where lengthy, complicated calculations, which describe physical processes, must be repeated frequently. � 2002 Elsevier Science Ltd. All rights reserved.

Directional Wind–Wave Coupling in Fully Coupled Atmosphere–Wave–Ocean Models: Results from CBLAST-Hurricane

AbstractThe extreme high winds, intense rainfall, large ocean waves, and copious sea spray in hurricanes push the surface-exchange parameters for temperature, water vapor, and momentum into untested regimes. The Coupled Boundary Layer Air–Sea Transfer (CBLAST)-Hurricane program is aimed at developing improved coupling parameterizations (using the observations collected during the CBLAST-Hurricane field program) for the next-generation hurricane research prediction models. Hurricane-induced surface waves that determine the surface stress are highly asymmetric, which can affect storm structure and intensity significantly. Much of the stress is supported by waves in the wavelength range of 0.1–10 m, which is the unresolved “spectral tail” in present wave models. A directional wind–wave coupling method is developed to include effects of directionality of the wind and waves in hurricanes. The surface stress vector is calculated using the two-dimensional wave spectra from a wave model with an added short-wave s...

Effect of Surface Waves on Air–Sea Momentum Exchange. Part I: Effect of Mature and Growing Seas

The effect of surface waves on air‐sea momentum exchange over mature and growing seas is investigated by combining ocean wave models and a wave boundary layer model. The combined model estimates the wind stress by explicitly calculating the wave-induced stress. In the frequency range near the spectral peak, the NOAA/ NCEP surface wave model WAVEWATCH-III is used to estimate the spectra, while the spectra in the equilibrium range are determined by an analytical model. This approach allows for the estimation of the drag coefficient and the equivalent surface roughness for any surface wave fields. Numerical experiments are performed for constant winds from 10 to 45 m s21 to investigate the effect of mature and growing seas on air‐sea momentum exchange. For mature seas, the Charnock coefficient is estimated to be about 0.01; 0.02 and the drag coefficient increases as wind speed increases, both of which are within the range of previous observational data. With growing seas, results for winds less than 30 m s 21 show that the drag coefficient is larger for younger seas, which is consistent with earlier studies. For winds higher than 30 m s 21, however, results show a different trend; that is, very young waves yield less drag. This is because the wave-induced stress due to very young waves makes a small contribution to the total wind stress in very high wind conditions.