Theoretical derivation and experimental validation of tree detection rate in TLS-based forest plot surveys

Terrestrial laser scanning (TLS) has been widely used in forest inventories, where tree detection rate serves as a key indicator of scanning efficiency. However, limited research has focused on the quantitative correlation between plot design and detection rate. In this study, we systemically investigate how plot characteristics-including plot size, stem density, and diameter at breast height (DBH)-affect tree detection rate, using a combined approach of theoretical derivation, simulated point clouds, and field measurements. Based on scanning geometry, we derive an analytical detection rate formula that accounts for inter-tree occlusion and spatial tree distribution to estimate tree detection probability. For simulation analysis, we generate point clouds for 1600 virtual plots with controlled gradients of plot radius (10-25 m), stem density (200-1400 stems ha^-¹), and DBH (0.1-0.4 m). The derived model is further validated using field TLS data from real forest plots. Results show that the theoretical detection rate estimates agree well with both simulated and field-measured values. The proposed formula can provide a reliable baseline for predicting detection rates in TLS plot scanning and support the optimization of forest inventory experimental design, demonstrating applicable practical value for operational forest surveys.