II. Total Stem Gross Cubic Foot Volume — Forked Trees 



The ratios of actual forked volume divided by predicted unforked volume were 

 plotted over d.b.h. (D) , total tree height (H) , position to fork (P) , and number of tips 

 (T) and examined for trends. From this examination, a set of 12 potential transforma- 

 tions on D, H, P, and T were developed and all possible combinations of three or less 

 were screened through program REX (Grosenbaugh 1967) . Selected models from this screen- 

 ing run were then tabled and the one with the lowest RMSQR that "behaved well" was 

 picked as the final model. (An equation was judged to "behave well" if it did not 

 produce unrealistic results over the expected range of usage and if it did not exhibit 

 an undulating behavior for different combinations of tree characteristics.) Yellow pine 

 was combined with blackjack pine, and white fir and Douglas-fir were pooled across 

 National Forests because of the need to strengthen the data sets. 



III. Merchantable Gross Cubic Foot Volume — Unforked Trees 



Expressing merchantable gross cubic foot volume as the' difference between total 

 stem gross cubic foot volume and the unmerchantable gross cubic foot volume in the top 

 and stump is a convenient technique for examining and then characterizing the effect of 

 changing top diameter upon merchantable gross cubic foot volume. To see this advantage, 

 consider the following: 



Unmerchantable Volume = (Top Volume) + '(Stump Volume) 



, X TT ^ /fop Diameter\^/Top length \ 

 ~ M X 144-' \ in Inches / \ in Feet / 



. TT /Stump Diameter\2/Stump Height] ... 



U X 144-' \ in Inches / ' in Feet / ^ ' 



where 



k - \ form factor. 



It has been shown that stump diameter and d.b.h. are highly correlated (Hann 19''6) and 

 it is also true that stump height is basically a constant; therefore, the second term 

 of equation (4) can be expressed as 



ao + ::iD2. (5) 



For top volume, the top diameter is specified by the user; therefore, the unknown quan- 

 tities are top length and the form factor, k. To help determine the relationship of top 

 length to d.b.h. and total tree height, the following model was fitted for each top 

 diameter: 



In(TL) = ao + ailn(D) + a2ln(H) (6) 



where 



TL = Top length in feet. 



33 



