Estimating the leaf area index of urban individual trees based on actual path length

The leaf area index (LAI) is an essential biophysical variable of trees and a crucial factor affecting the urban environment. Previous studies on LAI measurements mainly focused on continuous forests, which using the cosine of the observed zenith angle for path length correction is incompatible with individual trees, although individual trees are more common in urban areas. Therefore, we modified the Beer-Lambert law for individual trees and developed a new path length correction factor that considers crown shape and actual path length in this study. Based on the new path length correction factor, we proposed a systematic single-tree LAI estimation method using digital cover photography. Comparisons with measurements showed that the root mean square error (RMSE) and Pearson correlation coefficient (r) are 0.35 and 0.97, respectively. A Python scripted module was compiled to support automated processing of this method. Furthermore, we modeled single-tree crown transmissivity based on the new path length correction factor and provided a simple formula to calculate the transmissivity of the spherical crown using some common assumptions. This study offers a theoretical basis for measuring LAI and calculating the crown transmissivity of individual trees