Mechanistic Models of the Wind Speed Probability Distribution
While most studies of the wind speed pdf have been empirical, recent efforts have been made to develop physically based models ofp_{m}.(u, v) and p„,(w). Through this approach, the pdfs are expressed in terms of dynamically meaningful parameters rather than abstract statistical parameters. For example, Monahan used an idealized slab model of the sea surface boundary layer momentum budget driven by fluctuating largescale pressure gradients!^{91} to express p_{w}(w) in terms of the boundary layer depth, boundary layer top entrainment velocity, surface drag coefficient, and pressure gradient statistics.^{191} He et al. used a generalized version of this model^{181} to demonstrate that surface buoyancy fluxes and the character of the land surface have important influences on the pdf of wind speed.^{181} A subsequent analysis suggested that the long positive tail of the nighttime wind speed pdf is a result of intermittent turbulent mixing at the top of the normally quiescent nocturnal boundary layer.^{1201} Much more work remains to be done on this problem; the mechanistic study of surface wind pdfs remains in its infancy.
Conclusions
The wind speed probability distribution is a central ingredient in studies of wind hazards, wind energy assessment, and fluxes between the atmosphere and the underlying surface. While the structure ofp_{w}(w) can be constrained by some fundamental general requirements, it is not known to be fully characterized by any single family of distributions. Characterizations of p_{w}(w) can be empirical (by parametric distributions such as the Weibull), or derived from representations of the joint distribution of the vector wind components. An emerging area of study seeks to develop physically based models of p_{w}(w). These approaches offer distinct and complementary insights into the pdf of surface winds.
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