GENERAL USE OF THE LOGARITHMIC WIND PROHLE EQUATION 



According to several authors, the log-wind profile represents the actual wind pro- 

 file near the surface of the earth only under neutral stability condition. However, 

 various researchers have found that the log-wind profile represents the wind above a 

 vegetative cover (very rough surface) over a wide range of atmospheric conditions. For 

 example, van Hylckama (1970) reports that a log-wind profile represented the wind vari- 

 ation above a salt cedar stand {Tamavi-x pentandra) for all his afternoon observations 

 and for many night conditions. Of 744 data sets, only 84 were too irregular for log- 

 wind representation. Oliver (1971) found the wind profile above a pine forest to be 

 well described by the logarithmic form over a wide range of stability conditions. 



Apparently, large temperature gradients cannot be maintained above a forest canopy 

 due to air movement through the canopy (Munn 1966, p. 158) and due to mixing by which 

 the wind blowing over a very rough surface reduces air temperature variations above the 

 canopy. Thus extreme lapse or inversion temperature conditions are unlikely to obtain 

 over a vegetative cover, resulting in a broad applicability of the log-wind profile. 

 However, we advise that this form not be used to estimate winds under conditions of 

 strong surface air temperature inversions. In summer this happens most often at night 

 under clear skies with very low surface wind speeds. So when wind represents an impor- 

 tant influence on fire behavior, the log profile usually is applicable. 



WIND UNDER A CANOPY 



To model the variation of windspeed with height for air flow through and under a 

 forest canopy, we make several simplifying assumptions: 



1. Below some height, z^^ near but below the top (height H) of the uniform 

 forest canopy, the windspeed is approximately constant with height. 



2. The foliage vvrithin the height range from z^^^ do™ to the bottom of the 



live crowns at height z provides a bulk drag force that resists the 

 airflow. 



3. Shear stress (equal to that in the constant stress layer above) on the 

 surface z - balances the integrated bulk drag force in the constant 

 speed layer. 



The approximate windspeed profile is thus: 



(U./K) (VlSH^"^-) 



U(2) = 



M 



(10) 



The assumption of a constant windspeed beneath the canopy seems quite reasonable accord- 

 ing to various authors (Pons 1940, Geiger 1966, Shaw 1977) . Now the resistance to 

 airflow in the canopy can be expressed as a force/unit volume, R, due to drag on the 

 canopy foliage (conifer needles in most applications). The value of R is given by: 



R = 1 p An, (11) 



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