A Novel Data-Driven Approach to Leaf Area Index Modeling Using High-Fidelity Simulation-Based Full-Waveform LiDAR Data

Leaf area index (LAI), defined as the total one-sided leaf area per unit ground area, is a key parameter in forest eco-physiology and ecosystem modeling, linking leaf-level processes to canopy-scale gas exchange and energy fluxes. Conventional LAI estimation methods face various scalability and accuracy limitations, e.g., field-based approaches are constrained by labor-intensive data collection, while passive optical remote sensing suffers from documented spectral saturation in dense canopies. Full-waveform light detection and ranging (wLiDAR), which provides detailed vertical canopy structure, offers a scalable alternative to other sensing methods. This study presents a framework for LAI estimation using high-fidelity wLiDAR simulations that are representative of temperate forest canopy conditions, to evaluate two modeling paradigms: (1) an interpretable empirical model in a limited data regime using waveform-derived metrics, and (2) a data-driven convolutional neural network (CNN) in a larger data regime. The empirical model, based on Gini coefficient, waveform centroid, and total return energy, performed well in moderate canopy densities, with peak accuracy at intermediate footprint sizes ($\approx 20 \rm{ m}$). The CNN consistently outperformed both the empirical model and traditional off-the-shelf regressors- including Support Vector Machines (SVM), XGBoost, Random Forest, Gradient Boosting and ElasticNet - achieving an accuracy improvement of approximately$5-10\%$while maintaining robust performance across multiple spatial scales. These gains, however, come with increased model complexity, reduced interpretability and domain transferability, underscoring the continued value of empirical models in ecologically-complex scenarios characterized by heterogeneous canopy structure, mixed species composition, and variable leaf area distributions. Real-data validation using LVIS waveforms further demonstrated that both the empirical ($R^{2}$= 0.75, MSE = 0.05) and CNN ($R^{2}$= 0.50, MSE = 0.09) models generalize well to operational observations. Overall, this work validates both interpretable and deep learning approaches for LAI estimation from wLiDAR, highlights the influence of footprint size, and establishes a simulation-based framework applicable to airborne and spaceborne missions such as the Land, Vegetation, and Ice Sensor (LVIS) and Global Ecosystem Dynamics Investigation (GEDI) platforms.