Lidar remote sensing of forest biomass: A scale-invariant estimation approach using airborne lasers

Researchers in lidar (Light Detection And Ranging) strive to search for the most appropriate laser-based metrics as predictors in regression models for estimating forest structural variables. Many previously developed models are scale-dependent that need to be fitted and then applied both at the same scale or pixel size. The objective of this paper is to develop methods for scale-invariant estimation of forest biomass using lidar data. We proposed two scale-invariant models for biomass: a linear functional model and an equivalent nonlinear model that use lidar-derived canopy height distributions (CHD) and canopy height quantile functions (CHQ) as predictors, respectively. The two models are called functional regression models because the predictors CHD and CHQ are themselves functions or functional data. The model formulation was justified mathematically under moderate assumptions. We also created a fine-resolution biomass map by mapping individual tree component biomass in a temperate forest of eastern Texas with a lidar tree-delineation approach. The map was used as reference data to synthesize training and test datasets at multiple scales for validating the two scale-invariant models. Results suggest that the models can accurately predict biomass and yield consistent predictive performances across a variety of scales with an R2 ranging from 0.80 to 0.95 (RMSE: from 14. 3 Mg/ha to 33.7 Mg/ha) among all the fitted models. Results also show that a training data size of around 50 plots or less was enough to guarantee a good fitting of the linear functional model. Our findings demonstrate the effectiveness of CHD and CHQ as lidar metrics for estimating biomass as well as the capability of lidar for mapping biomass at a range of scales. The functional regression models of this study are useful for lidar-based forest inventory tasks where the analysis units vary in size and shape. They also hold promise for estimating other forest characteristics such as below-ground biomass, timber volume, crown fuel weight, and Leaf Area Index.