Predicting the number of trees in small diameter classes using predictions from a two-parameter Weibull distribution

Abstract

Summary Knowing the abundance of small trees is necessary for accurate calculation of gross production, total carbon and/or biomass of forest stands. The abundance of small trees can also be used to predict ingrowth into larger tree diameter classes. We present a method of predicting numbers of trees in small diameter classes using diameter distributions of larger trees in stands. A truncated two-parameter Weibull distribution was fit to large tree diameters (diameter at breast height (d.b.h.) ≥ 9.0 cm). These parameters were then used to predict the number of small trees in d.b.h. classes smaller than 9.0 cm. Three methods of predicting densities of small trees were used: (1) an extrapolation of the truncated Weibull to a full two-parameter Weibull distribution; (2) a modification of the Weibull using an empirical estimate and (3) a combined approach. While the full two-parameter Weibull distribution generally fitted the distribution of small trees, densities were typically under-predicted. The empirical method (i.e. method 2) produced the best predictions of small tree densities, with a root mean square error of 132 trees h 21 (28 per cent of mean small tree density). Overall, predicting the distribution of small trees using the distribution of large trees worked very well in this study.