LITIDA: a Cost-Effective Non-Parametric Imputation Approach to Estimate LiDAR-detected Tree Diameters over a Large Heterogeneous Area

The advent of light detection and ranging (LiDAR) technology has enabled accurate height measurements of individual trees; however, deriving tree diameters at breast height (DBH) from heights has proven challenging. Three issues exist: (1) reference errors caused by false data entries, incorrect measurements in the field, or the spatial mismatch of a LiDAR-detected tree to a field-measured tree, (2) general DBH underestimations for fully matured (FM)' trees with a saturating DBH-height relationship and (3) heterogeneity over expansive and diverse forested landscapes with corresponding variability in the DBH-height relationship. We addressed these three issues by developing the algorithm called LiDAR Individual Tree Imputed Diameter Algorithm (LITIDA). In LITIDA, the predictors include LiDAR-estimated tree height and plot-level climate, species composition, site index and competition stress. These predictors can be obtained without precise locations of measured trees; therefore, matching LiDAR-detected trees to field-measured trees is not necessary. For each individual LiDAR-detected tree, LITIDA is designed to select candidates from field-measured trees and adopt a weighted mean DBH to reduce the influence of outliers. Furthermore, larger DBHs are assigned to FM trees; therefore, DBH underestimation for FM trees can be mitigated. LITIDA is a non-parametric algorithm considering the biotic and abiotic variations that contribute to the complex DBH-height relationship; therefore, LITIDA can be applied over large and complex landscapes. The effectiveness of LITIDA was demonstrated on the Tahoe National Forest where 15 329 trees from 27 species over a 3526 km(2) area were measured in 544 plots. The DBH of more than 77 million trees were estimated. The 10-fold cross-validation resulted in root-mean-square error (RMSE), mean absolute error (MAE), and bias of 9.785 cm, 7.3 cm and -1.121 cm, with the relative error being 21.5 per cent, 16.1 per cent and -2.5 per cent, respectively. However, the actual accuracy for this demonstrative study was most likely higher because of reference data errors found in 30 of the 39 outliers in the reference tree database. We conclude that LITIDA is a cost-effective non-parametric imputation approach that can estimate LiDAR-detected tree diameters effectively over a large heterogeneous area.