How to better estimate leaf area index and leaf angle distribution from digital hemispherical photography? Switching to a binary nonlinear regression paradigm

Abstract

Probabilistic modelling of gaps for light-canopy interactions has long served as a theoretical basis to estimate vegetation structural parameters-leaf area index (LAI) and leaf angle distribution (LAD)-from optical measurements such as hemispherical photos. Direct inversion of such probabilistic models provides a reliable statistical algorithm for parameter estimation, but this inferential paradigm has been seldom explored. Even worse, many classical LAI algorithms implicitly assume "wrong" statistical models inconsistent with the underlying probabilistic gap models-a subtle issue not articulated before but known to cause practical issues. Here, we clarified how to improve LAI and LAD estimation by directly inverting binary gap/non-gap data of hemispherical photos via binary nonlinear regression (BNR). We implemented the new BNR method and some classical algorithms in an R package "hemiphoto2LAI", comprising a total of 135 models for LAI estimation. Compared to classical algorithms, BNR features many theoretical advantages and allows estimating LAI and LAD simultaneously. BNR can address questions difficult to answer by classical algorithms (e.g. how better is one LAD than another?). We demonstrated the utility of the BNR paradigm based on both synthetic and real data. Overall, BNR is statistically more justifiable but its potential has been under-appreciated. We encourage the community to embrace this new paradigm for reliable analyses of hemispherical photos or other gap data for canopy research.