## 1 Introduction

[2] Quantifying momentum transport resulting from turbulent mixing requires turbulent eddies to be explicitly resolved. Thus, in numerical prediction of weather and climate and many other applications in geosciences, the surface momentum fluxes are often determined parametrically in terms of mean wind speed

where *u*_{∗} and *U*_{10} are the friction velocity and 10-m wind speed, respectively. *C*_{D} is a dimensionless coefficient often called the drag coefficient in the literature [*Deardorff*, 1968]. Despite the simplicity of the concept, *C*_{D} cannot be determined by the bulk transfer model itself. In practice, the Monin-Obukhov Similarity (MOS) Theory [*Monin and Obukhov*, 1954] is often used to close the system to yield

where *z*, *z*_{0}, and *κ* represent the height, aerodynamic surface roughness, and Von Karman constant, respectively. is the dimensionless stability parameter, and *L* is the Obukhov length defined as , where *θ*_{0}, *g*, and are the surface mean potential temperature, gravity, and kinematic surface buoyancy flux, respectively. In this study, *L* is computed directly based on its definition from the surface fluxes determined by the eddy correlation method. Ψ_{m}(*ζ*) is an empirical stability function. *C*_{DN} is the drag coefficient in neutral conditions. Since the aerodynamic surface roughness is estimated within the same framework, to avoid redundancy, *C*_{DN} is often estimated directly from *C*_{D} corrected by stability as [*Grachev et al.*, 1998]

[3] To appropriately use equations (1) and (2) to parameterize surface momentum fluxes, there are issues that need be addressed. Over the ocean, the surface roughness depends on wind speed. Combining equation (2) with the Charnock formula [*Charnock*, 1955] for oceanic roughness, it can be shown that *C*_{DN} increases with wind speed. However, observations show that *C*_{DN} does not increase unlimitedly with wind speed; instead, it starts to level off at certain wind speeds [*Powell et al.*, 2003; *Black et al.*, 2007; *Donelan et al.*, 2004; *Drennan and Graber*, 1999; *Drennan et al.*, 2005]. Such a behavior of *C*_{DN} reflects the response of the ocean surface to the exerted winds. The aerodynamic roughness may attain a “saturated” state at a certain large wind speed since the ocean surface simply cannot be any rougher in an aerodynamic sense [*Donelan et al.*, 2004]. Although there exists a disagreement on the wind speed at which *C*_{DN} starts to level off, the change in *C*_{DN} from moderate to high wind speed can be well explained by MOS as long as the oceanic surface roughness can be accurately determined.

[4] For overland conditions, a large change in surface roughness with wind speed is not expected because of the static nature of the surface roughness elements. Equation (2) predicts a constant *C*_{DN} independent of wind speed for a fixed *z*_{0}, but this is not supported by observations. Figure 1 shows *C*_{DN} as a function of wind speed obtained from multiple independent field experiments for overland conditions [*Grachev et al.*, 2006; *Al-Jiboori*, 2010; *Mitsuta and Tsukamoto*, 1978; *Rao et al.*, 1996; *Mahrt et al.*, 2001; *Rao*, 2004] where *C*_{DN}, in some cases, is calculated based on equation (3), whereas in others, it is computed under near-neutral conditions. *C*_{DN} obtained from different experiments shows a large spread possibly due to the different land surface conditions in these studies. For example, the data in *Al-Jiboori* [2010] were collected in a complicated urban area. The large *z*_{0} leads to a large *C*_{DN}. Despite the large spread of *C*_{DN}, all the data show a clear trend of *C*_{DN} increasing with a decrease in wind speed. There have been attempts to explain the observed variation of *C*_{DN} with wind speed within the MOS framework. For example, *Mahrt et al.* [2001] argued that lower wind speeds enhance the viscous effects and reduce the streamlining of surface obstacles. The combined effect results in an increase in aerodynamic surface roughness as wind speed decreases. But, such an argument of attributing the observed variation of *C*_{DN} solely to the change in *z*_{0} with wind speed may lack legitimacy. From equation (2), one can readily calculate *z*_{0} required to obtain the values of *C*_{DN} represented by the best fit curve in Figure 1. There is a sharp increase of *z*_{0} as wind speed decreases, and it can reach up to 10 m for extremely low wind speeds, which is impossible for most of the overland conditions. Therefore, the objectives of this paper are to provide a physically sound explanation for the observed variations of *C*_{D} and *C*_{DN} and attempt to extend the classic MOS framework into the low-wind regime.