Predicting tree diameter using allometry described by non-parametric locally-estimated copulas from tree dimensions derived from airborne laser scanning

Abstract Biomass inventories that employ airborne laser scanning (ALS) require models that can predict tree diameter at breast height (DBH) from ALS-derived tree dimensions, as ALS can usually not directly measure DBH due to scanning angle, inadequate point density and canopy obstruction. Although some work has been done in using correlation as a measure of dependence to describe the linear relationship between variable means, none has investigated the copula-based measure of dependence for the prediction of DBH from ALS-derived height and crown diameter. Following the application of a locally-estimated copula method to 79 sample plots in eastern Finland, we compared the performance of the copula method with a baseline local regression (LOESS) model and an ordinary least squares (OLS) model. We found that the copula method outperformed the OLS model by decreasing 30% of the root-mean-squared error (RMSE). The copula method performed slightly better than the LOESS model for the original sample, but the results of the bootstrap samples showed that the variance in RMSE was sixteen times lower in the copula method than the LOESS model, suggesting that the copula had a more consistent and robust model performance across the 10,000 bootstrap samples. Moreover, while the LOESS model only predicts the conditional mean of the response variable, the copula method can also predict median and other quantiles.