Numerical Model of Marine Surface Winds and Its Application to the Prediction of Ocean Wind Waves

Abstract

Accurate and detailed es timation of marine surface winds is needed for the practical application of numerical models describing ocean wind waves and storm surges. Actual surface winds are essentially turbulent and variable because of the critical influence of complex surface structure, atmospheric stability, etc. Especially on the marine surface, parameterization of the winds requires ultimately a knowledge of the process of wave generation because of the mutual exchange of the momentum between winds and waves. So the theoretical estimation of real surface winds is very difficult and empirical formulas have been used for practical purposes.
Recently, BLACKADAR (1965) and CARDOND (1969) proposed a method of marine surface wind estimation based on a theoretical atmospheric boundary layer model. It is a two-layer baroclinic model for the marine boundary layer. The object of the present paper is to examine several features of their model and make an evaluation of it preliminary to operational use.
As seen in Fig.1, the atmospheric surface boundary layer is assumed to be separated into two regions: surface layer and Ekman layer. In the surface layer, the Coriolis parameter is neglected, the turbulent transfer coefficient for momentum (K_m) increases almost linearly with height, and the wind stress is constant. The vertical wind profile is represented by Equation (A.1.8) in this layer. The height of the surface layer (h) is assumed to be specified explicitly in terms of the external parameters, and Blackadar's formulation (2.1) is adopted. The effect of the wave motion on the structure of the surface wind is taken into consideration indirectly in the specification of the surface roughness parameter which is reprseented by Equation (A.1.27).
In the Ekman layer, K_m is constant, the wind stress decreases with height, and the geostrophic wind components u_g, υ_g and vg are assumed to be linear functions of height. The vertical wind profile is specified by Equation (A.1.30), which is the so-called Ekman's solution.
Equation (A.1.30) is connected with Equation (A.1.8) with the boundary condition (2.5) through the height h, and the inflow angle (ψ) and the friction velocity (U*) are represented at the height h by Equations (A.3.16) and (A.3.17) respectively. With the equations for stability length (A.1.12), friction velocity (A.3.17)and surface roughness parameter (A.1.27), the surface layer wind distribution is completely described. These three equations can be solved simultaneously for U* using the iteration technique which is shown in Fig.2.
Computation of the winds to examine the model was made over the Western North Pacific every six hours from 5, Jan.1972 through 12, Jan.1972. The input data are sea level pressure, sea surface temperature and surface air temperature at each of the grid points spaced 150 km apart.
In the prese n t paper, the computations at OOz,11, Jan.1972are described. Fig.9 shows the distribution of wind velocity which is computed by use of the two-layer surface wind model. Fig.10 is the distribution of wind velocity which is obtained from the analysis based on the ship observations. The frequency of the velocity difference between computed and analysed winds on the grid points is shown in Fig.11. The standard deviation of the velocity difference is 3.05 m/s, and the computed wind velocity is 1.77 m/s smaller than the analysed wind velocity on the average.
Fig.15 shows the relationships between the friction velocity and the surface wind speed.
The relationship obtained from the two-layer surface wind model agrees reasonably well with that obtained from the analysis of many observations by Kuznetsov (1970).
Two computations of ocean wind waves by the procedure of ISOZAKI and UJI (1973) were performed from 5, Jan.1972 through 12, Jan.1972. In Test-1, the wind data obtained by synoptic analysis based