| Home > Research > Ifsdocs > WAVES > |
Chapter 2. The kinematic part of the energy balance equation
Chapter 3. Parametrization of source terms and the energy balance in a growing wind sea
Chapter 4. An optimal interpolation scheme for assimilating altimeter data into the WAM model
Chapter 5 Numerical scheme
Chapter 6 The WAM-model software
Chapter 7 Wind-wave interaction at ECMWF
REFERENCES
Previous Section
1.2 Overview of this document
In this document we will try to make optimal use of the knowledge of wave evolution in the context of numerical modelling of ocean waves. However, in order to be able to develop a numerical wave model that produces forecasts in a reasonable time, compromises regarding the functional form of the source terms in the energy balance equation have to be made. For example, a traditional difficulty of numerical wave models has been the adequate representation of the nonlinear source term
. Since the time needed to compute the exact source function
expression greatly exceeds practical limits set by an operational wave model,
some form of parametrization is clearly necessary. Likewise, the numerical
solution of the momentum balance of air flow over growing ocean waves, as
presented in Janssen (1989), is by far too time consuming to be practical
for numerical modelling. It is therefore clear that a parametrization of
the functional form of the source terms in the energy balance equation is
a necessary step to develop an operational wave model.The remainder of this document is organised as follows. In Chapter 2 we discuss the kinematic part of the energy balance equation, that is, advection in both deep and shallow water, refraction due to currents and bottom topography. The next section, Chapter 3, is devoted to a parametrization of the input source term and the nonlinear interactions. The adequacy of these approximations is discussed in detail, as is the energy balance in growing waves. In Chapter 4 a brief overview is given of the method that is used to assimilate Altimeter wave height data. This method is called Optimum Interpolation (IO) and is a more or less one to one copy obtained from the work of Lorenc (1981). A detailed description of the method that is used at ECMWF, including extensive test results is provided by Lionello et al. (1992). SAR data may be assimilated in a similar manner. Next, in Chapter 5 we discuss the numerical implementation of the model. We distinguish between a prognostic part of the spectrum (that part that is explicitly calculated by the numerical model) (WAMDI , 1988), and a diagnostic part. The diagnostic part of the spectrum has a prescribed spectral shape, the level of which is determined by the energy of the highest resolved frequency bin of the prognostic part. Knowledge of the unresolved part of the spectrum allows us to determine the nonlinear energy transfer from the resolved part to the unresolved part of the spectrum. The prognostic part of the spectrum is obtained by numerically solving the energy balance equation. The choice of numerical schemes for advection, refraction and time integration is discussed. The integration in time is performed using a fully-implicit integration scheme in order to be able to use large time steps without incurring numerical instabilities in the high-frequency part of the spectrum. For advection and refraction we have chosen a first order, upwinding flux scheme. Advantages of this scheme are discussed in detail, especially in connection with the so-called garden sprinkler effect (see SWAMP, 1985, p144). Alternatives to first order upwinding, such as the semi-Lagrangian scheme which is gaining popularity in meteorology, will be discussed as well.
Chapter 6 is devoted to software aspects of the WAM model code with emphasis on flexibility, universality and design choices. A brief summary of the detailed manual accompanying the code is given as well (Günther et al. , 1992). Finally, in Chapter 7 we give a list of applications of wave modelling at ECMWF, including the two-way interaction of winds and waves.
Next Section
Previous Section
 |
23.04.2002 |
 |
© ECMWF |
