Joint Estimation of Leaf Area Density and Leaf Angle Distribution Using TLS Point Cloud for Forest Stands

Abstract

The foliage density $(u_l)$ and the leaf angle distribution (LAD) are important properties that impact radiation transmission, interception, absorption and, therefore, photosynthesis. Their estimation in a forested scene is a challenging task due to their interdependence in addition to the large variability in the forest structure and the heterogeneity of the vegetation. In this work, we propose to jointly estimate both of them using terrestrial laser scanner (TLS) point cloud for different forest stands. Our approach is based on direct/inverse radiative transfer modeling. The direct model was developed to simulate TLS shots within a vegetation scene having known foliage properties (i.e., $u_l$ and LAD) resulting in a 3-D point cloud of the observed scene. Then, the inverse model was developed to jointly estimate $u_l$ and LAD decomposing the 3-D point cloud into voxels. The problem turns out to a high-dimensional cost function to optimize. To do it, the shuffled complex evolution method has been adopted. Our approach is validated with results derived from several simulated homogeneous and heterogeneous vegetation canopies as well as from actual TLS point cloud acquired from Estonian Birch, Pine, and Spruce stands. Our findings revealed that our estimates were considerably close to the actual $u_l$ and leaf inclination distribution function (LIDF) values with ($\text{Biais}_{u_l} \in [0.001 \; 0.006]$, $\text{RMSE}_{u_l} \in [0.019 \; 0.045]$, $\text{RMSE}_{\text{LIDF}} \in [ 0.019 \; 0.038]$) for homogeneous dataset and ($\text{Biais}_{u_l} \in [0.001 \; 0.045]$, $\text{RMSE}_{u_l} \in [0.023 \; 0.078]$, $\text{RMSE}_{\text{LIDF}} \in [ 0.011 \; 0.018]$) for heterogeneous dataset with different tree crown geometries (i.e., conical and elliptical). In the actual case (Birch, Pine, and Spruce stands), our approach with the traditional and novel techniques, $\text{RMSE}_{\text{LAI}}$ are 0.526 and 0.105, respectively. The results outperform those of the baseline technique (i.e., assuming spherical LAD) with $\text{RMSE}_{\text{LAI}}=2.651$.

Keywords

• Leaf angle distribution (LAD)
• leaf area density
• leaf area index (LAI)
• leaf properties
• TLS
• voxel-based method