Table 12. — Coefficients for estimating In (foliage weight) of trees 

 less than 3.5 inches d.b.h.: 

 In(lVr) = bo, + b,ln(CL) + b2ln(4) + bjIniTPA) 





Variable coefficients 





Intercept 



In(CL) 



Species' 



bo, 



b. 



BP 



-2.81317 



1.47513 



WP 



-2.15894 



1 .48969 



WC 



-2.64034 



1 .69973 



WL 



-5.02156 



2.31835 



WH 



-4.22701 



2.22534 



AF 



-2.03919 



1 .64942 



LP 



-3.38394 



1 .96060 



GF 



-2.78090 



1 .90272 



ES 



-3.30673 



2.27613 



DF 



-2.30430 



1 .52896 



PP 



-3.02050 



1.88712 



Variables 



Variable coefficients 







bz = .22823 





\n(TPA) 



ba = - .13550 





Regression sum of squares d.f 

 Error sum of squares d.f. 

 Mean square error 



= 297.57812 23 

 = 44.17596 186 

 = 0.23751 

 = 0.8707 



'See text page 2 for species list. 



Residual sums of squares for prediction 

 of In (foliage weight) 



Current 

 models 



Browns 

 models 



Trees <3.5 

 inches d.b.h. 



44.17596 

 69.9460 



Trees S23.5 

 inches d.b.h. 



13.0346 

 10.08098 



Total 



57.21056 

 80.0269 



The current model for trees greater than or equal to 3.5 inches 

 (8.9 cm) d.b.h. had a larger residual sum of squares than that 

 obtained from Brown's methods. For trees less than 3.5 inches 

 (8.9 cm), residual sum of squares obtained by the present 

 method are lower. Overall there appears to be no loss in predic- 

 tive ability by using a single model form as presented here. 



Alternative Models for Foliage 

 Weight Prediction 



The prediction models for both large and small trees use the 

 variable In(age), which is not available in the prognosis system 

 (Stage 1973) in which the equations are to be used. Thus the 

 following alternative models are presented. 



For trees 3.5 inches (8.9 cm) and larger, the alternative model 

 is a transformation of the general model involving the diameter 

 and age terms. Periodic (diameter)^ increment, which is avail- 

 able in the prognosis model, is substituted for mean annual 

 (diameter)^ increment in the following transformation: 



ln(lV7) = bo, + biln(D) + b2ln(H) -r bjlniCL) + 

 bMA) +' b5ln(7P>4) + beHDREL) 



(general model in log linear form) 



or, 



l/VT = e °' ■ D''' • . (CLf3 . a^'^ ■ {TPAp ■ (DREL)^^ 

 (general model in exponential form) 



Multiplying by 



(b, - 2b ) 



(CLp. {TPAp- (DRELp 



which, in logarithmic form, is 



\r\{WT) = bo, + (bi + 2b4) ln(D) - b4 



+ b2ln(/-/) + b3ln(CL) + b5ln(rP-4) + beHDREL) 



'"(5) 



and substituting periodic [A (D^)] for mean annual [D^/A)] incre- 

 ment. 



\n(WTi = bo + (bi + 2b4)ln(D) - bMMO^)] ^ 

 bzHH) +b3ln(CL) +b5\n(TPA) - bMDREL) 



(alternative model) 



Kittredge (1944) noted that it would be expected that 'the 

 amount of foliage could be estimated from the periodic annual 

 growth because the increment of stem wood is determined by 

 the amount of foliage which is carrying on photosynthesis in that 

 period" (p. 906). It is important to note that the alternative model 

 has not been reparameterized with the periodic annual incre- 

 ment (PAI) as an independent variable since PAI was not mea- 

 sured. It is merely a transformation of the original parameters 

 and should be presented with a statement of caution about the 

 relationship between the mean annual increment (MAI) and 

 PAI. 



The substitution of periodic (diameter)^ increment for mean 

 annual increment in the alternative equation assumes that the 

 relationship between (diameter)^ and age is linear over a wide 

 range of ages. The assumption breaks down when PAI and MAI 

 diverge as typically happens over time except at the culmination 

 of MAI. Figure 1 shows the difference in predicted foliage weight 

 between the current and alternative models that can be ex- 

 pected when PAI departs from MAI. When PAI is 100 percent 

 greater than MAI, predicted foliage biomass increases 24 per- 

 cent. PAI 60 percent of MAI produces a 25 percent negative 

 change in predicted foliage biomass. 



11 



