Comparison of nearest neighbour approaches for small area estimation of tree species-specific forest inventory attributes in central Europe using airborne laser scanner data

The three nonparametric k nearest neighbour (kNN) approaches, most similar neighbour inference (MSN), random forests (RF) and random forests based on conditional inference trees (CF) were compared for spatial predictions of standing timber volume with respect to tree species compositions and for predictions of stem number distributions over diameter classes. Various metrics derived from airborne laser scanning (ALS) data and the characteristics of tree species composition obtained from coarse stand level ground surveys were applied as auxiliary variables. Due to the results of iterative variable selections, only the ALS data proved to be a relevant predictor variable set. The three applied NN approaches were tested in terms of bias and root mean squared difference (RMSD) at the plot level and standard errors at the stand level. Spatial correlations were considered in the statistical models. While CF and MSN performed almost similarly well, large biases were observed for RF. The obtained results suggest that biases in the RF predictions were caused by inherent problems of the RF approach. Maps for Norway spruce and European beech timber volume were exemplarily created. The RMSD values of CF at the plot level for total volume and the species-specific volumes for European beech, Norway spruce, European silver fir and Douglas fir were 32.8, 80.5, 99.0, 137.0 and 261.1%. These RMSD values were smaller than the standard deviation, although Douglas fir volume did not belong to the actual response variables. All three non-parametric approaches were also capable of predicting diameter distributions. The standard errors of the nearest neighbour predictions on the stand level were generally smaller than the standard error of the sample plot inventory. In addition, the employed model-based approach allowed kNN predictions of means and standard errors for stands without sample plots.