Estimation of diameter distributions by means of airborne laser scanner data

Abstract

Diameter distributions are an important source of information for estimating the timber assortment in forest stands. In this paper, a one-step procedure for deriving the parameters of a Weibull function, itself used to describe diameter distributions, is presented. A generalized linear model (GLM) is employed that allows for an estimation of the shape and scale parameters as functions of different predictors. The GLM was fit using 495 sample plots from a conventional sample-plot inventory. Plotwise height metrics derived from airborne laser scanner data serve as covariates (auxiliary variables). Each sample plot consists of four concentric circle plots, where the largest plot covers an area of 450 m2 (12 m radius). Trees with a diameter at breast height (DBH) <30 cm are measured only on the smaller circle plots. Because of this design, left- and right-truncated Weibull distributions, conditional on the DBH, were used to fit the data. The frequently used two-step procedure — in which the Weibull distribution is firstly fitted via maximum likelihood, and its parameters are then estimated via linear regression — requires an adequate number of observations per sample plot in the first step. Hence, this method would have been unsuitable for the data source at hand, because a mean of just 12 trees per sample plot was recorded. The visual comparison of the predicted Weibull distributions with observed data shows a good fit to the data. The mean of the DBH distributions was estimated with a root mean square error (RMSE) of 2.44 cm and a bias of 0.41 cm.