Model Validation 



The validity of our height growth models is most 

 legitimately ascertained by comparing them to height 

 growth models developed by stem analysis procedures. 

 Monserud's (1984b) Douglas-fir height growth model 

 developed for virtually the same geographic area as our 

 study qualifies as the most appropriate one for compari- 

 son; we assume that Monserud's height growth curves 

 represent the true Douglas-fir growth pattern against 

 which our height projection curves will be compared. 

 Figure 19a shows the height growth pattern pwedicted 

 by Monserud's (1984b> equations for three site index 



140 



u. 



40 60 80 100 120 140 160 180 200 



AGE OF PREDICTED SPECIES, YRS 



Figure 12.— Grand fir at site 

 index 60 is used to project the , 

 heights of Douglas-fir, 

 Engelmann spruce, and western 

 larch; heights of the associated 

 species are projected over their 

 sampled age ranges. 



h140 

 u. 



o120 



UJ 

 X 



40 60 80 100 120 140 160 180 200 



AGE OF PREDICTED SPECIES, YRS 



Figure 14.— Mountain hemlock at 

 site index 50 is used to project 

 the heights of Engelmann 

 spruce, lodgepole pine, and 

 subalpine fir; heights of the 

 associated species are projected 

 over their sampled age ranges. 



values, 40, 60, 80 (poor, medium, and high quality sites); 

 for these Douglas-fir site index values we have used 

 corresponding western larch site index values (derived 

 from table 2) and Douglas-fir age (table 3) to predict 

 Douglas-fir height. From ages 50 to 160 years (the 

 stipulated age range of equation applicability) the degree 

 of correspondence between the curves appears high. Our 

 equation overestimates Douglas-fir height by an average 

 of 4.0 feet at site index 80 and underestimates by 

 1.5 feet at site index 60 and 2.4 feet at site index 40. As 

 age increases beyond 150 years, our model produces 

 underestimates of increasing magnitude for all site index 

 values. Figfure 19b compares Monserud's (1984b) curves 



^140 



40 60 80 100 120 140 160 180 200 



AGE OF PREDICTED SPECIES, YRS 



Figure 13.— Lodgepole pine at 

 site index 60 is used to project 

 the heights of Douglas-fir, 

 Engelmann spruce, mountain 

 hemlock, subalpine fir, and west- 

 ern larch; heights of the 

 associated species are projected 

 over their sampled age ranges. 



20' I I I M M M M M M M M M M M M M M I 

 20 40 60 80 100 120 140 160 180 

 AGE OF PREDICTED SPECIES, YRS 



Figure 15.— Subalpine fir at site 

 index 50 is used to project the 

 heights of Engelmann spruce, 

 lodgepole pine, and mountain 

 hemlock; heights oi the 

 associated species are projected 

 over their sampled age ranges. 



9 



