Comparison of linear and mixed-effect regression models and a k-nearest neighbour approach for estimation of single-tree biomass

Allometric biomass models for individual trees are typically specific to site conditions and species. They are often based on a low number of easily measured independent variables, such as diameter in breast height and tree height. A prevalence of small data sets and few study sites limit their application domain. One challenge in the context of the actual climate change discussion is to find more general approaches for reliable biomass estimation. Therefore, nonparametric approaches can be seen as an alternative to commonly used regression models. In this pilot study, we compare a nonparametric instance-based k-nearest neighbour (k-NN) approach to estimate single-tree biomass with predictions from linear mixed-effect regression models and subsidiary linear models using data sets of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) from the National Forest Inventory of Finland. For all trees, the predictor variables diameter at breast height and tree height are known. The data sets were split randomly into a modelling and a test subset for each species. The test subsets were not considered for the estimation of regression coefficients nor as training data for the k-NN imputation. The relative root mean square errors of linear mixed models and k-NN estimations are slightly lower than those of an ordinary least squares regression model. Relative prediction errors of the k-NN approach are 16.4% for spruce and 14.5% for pine. Errors of the linear mixed models are 17.4% for spruce and 15.0% for pine. Our results show that nonparametric methods are suitable in the context of single-tree biomass estimation.