where z0 is the roughness scale without wave-induced currents, ub is the magnitude of the wave-induced bottom current, u*c is the mean friction velocity due to the mean current, ks 30z0 is the Nikuradse equivalent roughness, is the angle between the mean current and wave propagation direction, and Ab ub/ , with being the wave frequency. Of the parameters that affect function F, the most important are ub/u*c and Ab/ks; parameter has a somewhat weaker influence. Mellor (2002, henceforth M02) has applied a secondmoment closure-based turbulence model (Mellor and Yamada 1982) to oscillatory bottom boundary layers. He simulates a purely oscillatory boundary layer and demonstrates that the resulting numerical model velocity profiles compare reasonably well to the laboratory data of Jensen et al. (1989). He then applies the same method to oscillatory flows superimposed on a mean flow and plots z0a /z0 as a function of ub/u*c for various values of A/z0. However, he does not compare his results with published data on apparent roughness. Instead, he compares them with the analytical results of Grant and Madsen (1979, 1986, henceforth GM) plotted the same way (his Fig. D1). He concludes that his curves are shifted to the right vis-a-vis GM curves. This of course means that for the same values of ub/u*c and A/z0, M02 underestimates the increase in roughness due to wave-induced motions by roughly an order of magnitude. For example, for ub/u*c 20 and 0, M02 yields z0a /z0 3.4, whereas GM yields z0a /z0 69 for z0/Ab 10 . If z0/Ab is decreased to 10 , M02 value is substantially unchanged while GM yields z0a /z0 693. The study raises several questions. First, how do M02 results compare with published data? Does GM theory, the accepted standard for the past two decades, perform better? Is there anything that can be done to improve the agreement with data? This note is an attempt to answer these questions. Considerable effort has gone into determining the form of function F in Eq. (1). Because it is hard to estimate z0 from field experiments and hence z0a /z0, only laboratory experiments (Kemp and Simons 1982, 1983; Asano et al. 1986; van Doorn 1981, 1982; Sleath 1990) have provided a reliable means of estimating z0a /z0. Figure 1a shows z0a /z0 plotted against ub/u*c; Fig. 1b shows z0a /z0 plotted against (ub/u*c)(Ab/ks) . Sleath (1991) has suggested the following empirical relationship: