Comment on “A study of the slope probability density function of the ocean waves from radar observations” by D. Hauser et al.

[1] Intermediate-scale waves (ISW, about 0.02 to 6 m long) are the main contributor of the ocean surface roughness relevant to passive and active microwave remote sensing of the ocean. While wind speed is the most important parameter determining the spectral composition of the ocean surface roughness, analysis of field measurements indicates that the wave spectrum of ISW is strongly modified by background waves. The mean square slope derived from the wave spectrum is, therefore, also modified by the background wave condition. Investigation of ocean surface roughness without taking into account the sea state parameter can lead to incorrect conclusions. [2] The paper by Hauser et al. [2008] (hereinafter referred to as HCGM08) presented very interesting results on the properties of ocean surface roughness derived from C-band (5.35 GHz) radar observations. They compared the filtered mean square slope obtained under the assumption of Gaussian probability density function (pdf) of surface slopes with three published spectral models. Their interpretation of the empirical spectral model of Hwang [2005] (hereinafter referred to as H05) is inaccurate. As a result, they attributed the disagreement between their data with H05 to the discontinuity in the H05 spectrum caused by matching the empirically parameterized intermediate-scale wave (ISW) spectrum and an assumed equilibrium spectrum for the longer waves. The issue of matching will be further discussed in Section 2. Their description on the comparison with H05 was verbal (HCGM08, p. 9), the result is shown in Figure 1 here. The analyses of HCGM08 produced two sets of mean square slope (mss) as a function of wind speed based on the assumption of Gaussian (shown in their Figure 6d) and nonGaussian (their Figure 11b) surface slope pdf. They have noticed the large difference between the two sets of mss but no further comment or explanation was offered. Derivation of ocean surface roughness from radar backscattering cross section is a complex topic. Extensive discussions on the subject have been given in earlier publications [e.g., Jackson et al., 1992;Walsh et al., 1998]. Results of mss computation using essentially the same approach of HCGM08 by Jackson et al. [1992] for Ku band (14 GHz) andWalsh et al. [1998] for Ka band (36 GHz) are also shown in Figure 1, together with the sun glitter data of Cox and Munk [1954] and the filtered mss of H05 spectral model integrated to an upper cutoff wave number, kc, suggested by Jackson et al. [1992]. This cutoff wave number corresponds to surface wavelength about 4.7 times the radar wavelength. The cutoff wave number used by HCGM08 is much higher (corresponding to surface wavelength about 2.2 times the radar wavelength). For their C-band radar frequency (5.35 GHz), kc is 24 rad/m on the basis of the criterion of Jackson et al. [1992] and 51 rad/m on the basis of HCGM08. Also shown in their Figure 1 are the filtered mean square slope derived from direct inversion of the backscattering cross section of Ka band radar reported by Vandemark et al. [2004]. Further discussion of these data is deferred to Section 3. [3] After a close examination of their experimental conditions, it becomes clear that the source of disagreement is quite different from that suggested by Hauser et al. and the hint was in fact given in H05, that is, the mean square slope of the ocean surface is significantly modified by background waves. HCGM08 did not provide too much information about the wind and wave conditions of their experiment. However, on the basis of the tabulated data presented in an earlier paper of the same experiment [Mouche et al., 2005], the wavefields are strongly influenced by swell not related to the local wind condition. In contrast, the database used in constructing the H05 spectrum is wind-sea dominant with mild swell presence (Section3).Because radar remote sensingplays an increasingly more important role in oceanographic research and environmental monitoring, and that an accurate interpretation of the remote sensing measurement requires a correct understanding of the ocean surface roughness in response to various geophysical parameters of interest, such as wind, air-sea stability condition, waves of various scales and currents of various sources, a clarification of the properties of the ocean surface roughness spectrum is important. I hope this note serves to correct the misinterpretation given by Hauser et al. [2008] regarding the ocean surface roughness spectrum and to call attention the important role of a missing parameter – the background wave condition – in their analysis.