where 



p is the air density 



windspeed in canopy 



Cp the average drag coefficient (random foliage orientation) 

 A the side view area of needle = CD [length x diameter) 

 n is the average number of needles per unit volume 



TT 9 — 



n D^£ = 6, the average "packing ratio" (Rothermel 1972) (1 2" 



thus 



nA - n ^ £ • - — (13) 



where a is the surface-area-to-volume ratio of a single needle. This bulk resistive 

 force, integrated over the 

 (t) for the upper surface: 



force, integrated over the height range to z^^^, provides the shear stress requirement 



T = R -(z,, - zj (14) 



Since at z,, the shear stress is assumed to be that of the constant-shear layer, we have 

 M ^ 



T = p U2 (15) 



and so 



U2 Cp 30/2^ = p U2 (16) 



From this last expression and equation (3) we find 



(v^h)' = 2.K2/ (c, 30 (z, - zj) (17) 



For a uniform stand of nearly identical trees we can replace z,, - z by H-(CR) where H 



^ M m 



is tree height and CR is the crown ratio. Likewise, the average packing ratio, 

 can be expressed as 



3" = F3 (18) 



where 3 is the packing ratio for a single tree crown and F is the fraction of the canopy 

 layer filled with tree crowns. The fraction F is to be approximated by the product of 

 crown closure and a fraction accounting for the tapering of crowns that results in addi- 

 tional void volume higher in the canopy. Finally, the product of F and CR can be 

 represented by f, a fraction that represents the portion of volume under the canopy 

 top that is filled with tree crowns. 



7 



