Wind stress

The zonal and meridional components of the wind stress are defined, respectively, by

The air density, including the effect of moisture, is given by

The drag coefficient is parameterized as , where is the neutral drag coefficient and is a stability correction depending on the Monin-Obukhov length. The neutral drag coefficient formulation is based on Large and Pond (1981) modified for low wind speeds as in Trenberth et al. (1990):

Details of the surface layer formulation are given in Appendix A. The stability dependent drag coefficient is a function of several surface marine variables:

where

Analysis of the functional form of indicates that for the observed range of parameters, the linear dependence of on wind speed is the most important; the thermodynamic quantities only enter through the boundary layer stability correction.

As seen from the expressions above, the computation of wind stress requires simultaneous observations of the following quantities: , , , , and . In practice it is difficult to obtain complete ship reports, and cases in which one or more of the above quantities is missing are very common (Cardone et al. 1990). In order to circumvent the problem, wind stress is computed for all ship reports in which the wind data are available (neither missing nor trimmed by the quality control procedure). If the thermodynamic quantities are available, then they are used to compute . Otherwise the missing thermodynamic quantities are filled in with the analyzed monthly mean for that particular month. The accuracy of using monthly means in the calculation of this stability correction is discussed by Esbensen and Reynolds (1981).

Also note that the formulation for wind stress neglects the effects of the ocean's surface current. Over much of the ocean, wind speed is one or two orders of magnitude greater than the surface current. The surface current can be neglected in such circumstances. In the tropics, however, wind speeds are low and current speeds can be high. Halpern (1988) estimated the uncertainty in zonal wind stress due to the surface current is 17%in the tropics. Unfortunately, COADS/CMR-5 does not include surface current information. However, wind stress calculated from visually estimated winds will include current effects. Wind stress calculated with measured winds will contain error, but the degree of error is mitigated by a ship's tendency to drift with the current (W. Large, personal communication). The zonal wind stress values in this atlas series, therefore, presumably contain only a small degree of uncertainty in the tropics.