Nonlinear mixed-effects height to crown base model based on both airborne LiDAR and field datasets for Picea crassifolia Kom trees in northwest China

Height to crown base (hcb) is an important tree-level characteristic used for determination of crown size and for prediction of the initiation and propagation potential of crown fires. Crown size variables are often used as input variables for forest growth and yield models. In this study, a nonlinear mixed-effects hcb model was developed using measurements from 510 Picea crassifolia Kom trees in 16 sample plots in the Xishui forest farm of SunanYuguzu Autonomous County, Gansu Qilian Mountain National Nature Reserve, China. The modeling data were based on the airborne light detection and ranging (LiDAR), which serves as a reliable database for large forest areas. In general, field-based measurements are considered relatively more accurate compared with remote sensing data, but the LiDAR database can be applied for large forest area at a relatively low inventory cost when appropriate hcb prediction models are available. Given that measurements from the same sample plots were significantly correlated, we incorporated the random-effect component in the model to account for hcb variations at the sample plot-level. Among several potential predictors evaluated, we observed that diameter at breast height, LiDAR-derived total tree height, LiDAR-derived crown width, and LiDAR-derived plot dominant tree height were highly significant in the nonlinear mixed-effects hcb model. Four strategies for selection of sample trees per sample plot (largest trees, medium-sized trees, smallest trees, and randomly selected trees) and seven sample sizes (two to eight selected trees per sample plot) were evaluated for calibration of our nonlinear mixed-effects hcb model. The empirical best linear unbiased prediction method was applied to estimate the random effects for calibration and sample plot-specific hcb prediction. Calibration results revealed increased accuracy with increased number of selected trees per sample plot. However, selecting many sample trees per sample plot to calibrate the nonlinear mixed-effects hcb model may increase inventory costs with little gain in accuracy. Therefore, we recommended, in our study, that selection of five medium-sized trees per sample plot provides a compromise between measurement cost, model use efficiency, and prediction accuracy.