Crown structure in western hemlock, Douglas-fir, and grand fir in western Washington: horizontal distribution of foliage within branches

Horizontal distribution of foliage within individual branches was explored for three major tree species (western hemlock (Tsuga heterophylla (Raf.) Sarg.), Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), and grand fir (Abies grandis (Dougl. ex D. Don) Lindl.)) in the Pacific Northwest. Weibull, beta, normal, and Johnson's S(B) distributions were assessed for their ability to conform to the empirical foliage distributions. Moment-based parameter recovery and parameter prediction methodologies were applied. On the basis of the rank of individual branch x2-values, the beta distribution performed best under parameter recovery, while Johnson's S(B) distribution was best in terms of total sum of x2-values. Overall, few differences between the four distributions were observed. A system of moment-based parameter prediction equations was developed from branch dimensional and positional measures. The prediction equations showed that the ratio of relative distance from the stem to mean foliage density increased with increasing branch size. This relative increase was enhanced with increasing depth into crown for western hemlock, but not for Douglas-fir or grand fir. Again, the beta distribution, based on predicted moments, followed most closely the empirical distributions on the basis of the ranks of x2-values. The normal distribution was the best in terms of total sum of x2-values. As expected, moment-based parameter recovery produced smoothed distributions that followed more closely the observed empirical distributions; however, parameter prediction provides a methodology for predicting distributions when empirical moments are not available. No significant (p > 0.05) differences in horizontal foliage distribution were found between sites or fertilization treatments.