Modelling tree diameter from airborne laser scanning derived variables: A comparison of spatial statistical models

Formerly, tree height has been more difficult to measure accurately in the field than tree diameter at breast height. As a consequence, models to predict height from diameter measurements have been widely developed in the forestry literature. Through the use of airborne laser scanning technology (e.g., LiDAR), tree variables such as height and crown diameter can be measured accurately, a development which has spawned the need for models to predict diameter from airborne laser-derived measurements. Although some work has been done for fitting such models, none have incorporated spatial information to improve the accuracy of the predicted diameters. Using a simple linear model for predicting tree diameter from laser-derived tree height and crown diameter measurements, we compared the performance of ordinary least squares (OLS), generalized least squares with a non-null correlation structure (GLS), linear mixed-effects model (LME), and geographically weighted regression (GWR). Our data were obtained from 36 sample plots established in Norway. This is the first study to examine the use of spatial statistical models for tree-level LiDAR data. Root mean square prediction errors in tree diameter with LME are 3.5%, with GWR are 10%, and with OLS and GLS are 17%. LME also exhibited low variability in predicting performance across all the validation classes (based on laser-derived height). Giving the difficulties of using parametric statistical inference (such as maximum likelihood-based indices) for GWR, we used permutation tests as a way for detecting statistical differences. LME was significantly better than the other models, as well as GWR was to OLS and GLS. Our results indicate that the LME model produced the best predictions of tree diameter from LiDAR-based variables to a degree that has previously not been possible.