1/ Table 2--Values for a and b by years for the family of regressions for estimating height of the tallest trees in a newly established stand of Douglas-fir east of the Cascades where site index and age are known 4.407 0.149 3.924 0.182 -.422 .446 -.683 .659 -1.781 .680 -1.795 .849 -1.279 .866 -1.166 1.000 .172 1.013 .348 1.869 1.120 2.069 1.131 2.270 70 3.906 1.216 4.110 1.225 4.315 1.233 5.916 1.293 6.110 1.300 6.303 1.306 7.779 1.354 7.954 1.359 8.126 1.365 9.420 1.403 3.216 0.214 2.575 0.245 1.997 0.276 1.475 0.306 1.006 0.335 0.586 0.364 0.209 0.392 .472 -.911 .497 -1.108 .522 -1.127 .546 -1.418 .570 -1.534 .615 -1.698 .637 .593 -1.627 .700 -1.192 .720 -1.773 .740 -1.740 .759 -1.692 .778 -1.632 .796 -1.560 .814 -1.477 .832 .882 -1.045 .898 -.915 .913 -.778 .929 -.634 .944 -.484 .958 -.328 .972 -1.166 .986 1.026 .578 1.039 .711 1.051 .898 1.064 1.087 1.075 1.279 1.087 1.474 1.098 1.141 2.473 1.151 2.676 1.161 2.881 1.171 3.085 1.181 3.290 1.190 3.495 1.199 4.518 1.241 4.721 1.249 4.923 1.257 5.124 1.264 5.324 1.272 5.523 1.279 5.720 1.286 6.494 1.313 6.684 1.319 6.871 1.325 7.057 1.331 7.241 1.337 7.422 1.343 7.601 1.349 8.297 1.370 8.465 1.375 8.630 1.380 8.793 1.385 8.954 1.389 9.112 1.394 9.267 1.398 1.670 1.110 3.701 1.208 1/Height at a future date of the tallest portion of a young stand may be estimated on land of known site index by selecting a and b values for the appropriate breast-high age. Substitute a1 and b1 values in the equation, Height 4.5 feet a1 + b1 (site index 4.5 feet), for the particular breast-high age wanted. For example, for the height of the tallest tree in the stand at breast-high age 85 on land with a known site index of 100, solve the equation, HT - 4.5 6.871+ 1.325 (100 - 4.5), for a total height of 137.9 feet. Application In this study, site index is a number representing the height of the tallest tree for its breast-high age of 50 years on a 1/5-acre plot. Since site has been found to be closely correlated with volume (Spurr 1952), site index (as discussed here) will later be used in a yield. study to categorize volume productivity potentials of managed stands of Douglas-fir east of the Cascades. Height objectively reflects site where undamaged stands are not overstocked. Stands managed for maximum production of usable wood, in contrast to natural stands, probably will not be overstocked to the point of substantially reducing height growth. Therefore, use of these curves should be restricted to even-aged stands where height growth competition between trees has been held to a minimum. Appendix For both site index and height growth curves, a curve of average height for the samples as a function of age at 4.5 feet is constructed. This height curve is then adjusted to the desired site index, using the linear relationship existing between height and site index at any age, with appropriate estimates of slope and intercept. The curves are different because slope and intercept values of the equations are different for all ages except the index age (50 years for these curves). SITE INDEX CURVE CONSTRUCTION 1. For the site index curves, the tallest heights (HT) at each decade were read from the freehand curves and related to the site index (SI) for each plot by the equation, The 10 sample plots with a bh age of 90 or more years have site indexes of 54.3, 55, 65.2, 69, 69.2, 81.8, 91, 91.6, 95, and 97.4 feet. 2. The above decadal estimates of b were smoothed over age (fig. 4) by the equation (forced though a b value of 1 at a breast-high age of 50 years), where age here and in the equations to follow is breast high age. The standard error5 and R2 values for this equation are 0.0213 and 0.9994, respectively. 5 Standard error in this paper used with nonlinear equations is equal to ( (y - ŷ)2/(n - k))0.5; where y and ŷ are actual and predicted values, n is the number of points used to fit the curve, and k is the number of parameters that have been estimated in fitting the regression (Snedecor and Cochran 1967, p. 385). The resulting b values are those appearing in table 1. 3. 6 The following equation (with a standard error of 0.54 feet and an R2 of 0.9999), expressing decadal mean heights as a function of age, was conditioned to pass through mean site index (SI = 84.47) at 50 years (fig. 5): HT = . (-0.37496 + 1.36164 (log age) -0.00243434 (log。age)4). Here HT is an estimate of HT. At ages beyond 50 years, the sample became progressively smaller and mean site index was slightly different. Average heights were adjusted to the mean overall site index using 1 and b1 values of the individual regressions of 6 2 These standard errors and R values are for the equation as written, not its logarithmic form. 4. HT and the smoothed slope b of regressions for each year were then used to calculate the corresponding intercept a: 5. Substituting expressions for a, b, and HT in the basic equation of step 1 gives the final equation used to estimate site index as a function of breast-high age and height (fig. 3). 0.37496 + 1.36164 (log age) -0.00243434 (logage)*) 4 (0.52032 0.0013194 age + 27.2823/age) + (HT - 4.5) (0.52032 - 0.0013194 age + 27.2823/age). |