The development of allometric systems of equations for compatible area-based LiDAR-assisted estimation

Light detection and ranging (LiDAR) is used to estimate tree, stand and forest characteristics across large geographic areas. In most analyses, several independent LiDAR-based allometric equations are built to predict various forest attributes. When each forest attribute is estimated independently, there is potential for predictions of forest attributes that are not mathematically or biologically consistent. Combined allometric equations can be considered a system of equations describing the stand structure. Mathematically compatible and biologically meaningful estimates can be derived by estimating key structural variables and solving for other components, rather than estimating each forest attribute separately and independently. In this study, we propose the development of a system of allometric equations describing the relationship between volume per unit area, Lorey’s average height, basal area, quadratic mean diameter (QMD) and density. The system of allometric equations is derived from extensive field data. Key structural attributes are predicted using LiDAR metrics, and the remaining structural variables are solved for using the system of allometric equations. Predictions of structural attributes from the system of allometric equations are compared with predictions from independent LiDAR-derived prediction equations. Results showed that applying the systems approach can provide reasonable and compatible estimates with lower required sample sizes, especially when multiple attributes need to be considered simultaneously. Testing the portability of the systems approach in more complex stand structures and across different LiDAR acquisitions will be required in the future.