APPENDIX H 



DEVELOPMENT OF HEIGHT EQUATIONS 

 Even-aged Height Equation 



An examination of the Taylor Woods height data shovved that average diameter class height 

 increased asymptotically to the height predicted by Minor's (1964) height equation, as the 

 diameter class size approached the maximum for the stand. Functionally, this behavior can be 

 expressed: 



Hp = MH - i)i(MH-4.5)(1.0 - . 



With this function, average height of the diameter class (H^) approaches the height predicted 

 by Minor's (1964) equation (MH) as diameter class size (D) approaches the maximum diameter 

 class size that the stand has achieved in its development (DM) . Conversely, H^ approaches 

 4.5'2?i as D approaches zero. How quickly H approaches H^ depends upon the value of n; the 

 larger its value the quicker H will approach H^ as D increases. 



The following model was used to determine the appropriate values of bi and n: 



H -4.5 n 



By varying n between 1.0 and 2.5 at increments of 0.05, 30 different independent variables were 

 formed. An all-combination screening run using least squares regression through the origin was 

 then used to first select the best value of n and then to compute the regression parameter (2?;^) . 

 The resulting RMSQR for the final model was 0.1419. 



Uneven-Aged Height Equation 



A number of model forms have been proposed for characterizing height as a function of 

 diameter, including: 



Ti A r ao(D+K) ^ 



H=4.5+ai*e^^^ (1) 



ib3(inD)2 



H = 4.5 + bi'D^-e (2) 



The parameters K and m of model (1) have either been fixed at values of zero and one respec- 

 tively (Curtis 1967; Embry and Gottfried 1971; Burkhart and Strub 1974), or they have been 

 included as regression parameters (Monserud 1975) . Values of the parameters have been deter- 

 mined either through the logarithm transformation and linear regression process for models (1) 

 and (2) (Curtis 1967; Embry and Gottfried 1971; Burkhart and Strub 1974), or they have been 

 determined through nonlinear regression for model (1) (Monserud 1975). 



To incorporate the expected effect of site index upon these height-diameter models, the 

 following models were designed: 



C3(D+K)""' 



H = 4.5 + ci'S'^^-e (3) 



H = 4.5 . di.S^2./3-S.(D.K) 



-m 



(4) 



H = 4.5 + ei*S ^'D ^-e ^ (5) 



87 



