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.

Accelerating Leaf Area Measurement Using a Volumetric Approach

“…The water temperature was also recorded regularly. Volumetric calculations for the leaf pile was as follows: (11) where 𝑉 𝑙 and 𝑉 𝑟 are the volumes of leaf and retainer (mm 3 ), 𝜌 𝑇 is the water density (g/mm 3 ) at 𝑇 °C, and 𝑊 𝑙1 , 𝑊 𝑇2 , and 𝑊 𝑟2 are the weight (g) of leaf sample out of water, the underwater weight of the total immersed set (retainer and leaf sample), and the underwater weight of retainer, respectively. So, having the fix values of 𝑊 𝑟1 and 𝑉 𝑟 , it is enough to record three parameters of 𝑊 𝑙1 , 𝑊 𝑇2 , and water temperature in each running of the leaf volumetry.…”

“…Although at the present, various non-destructive techniques and tools have been introduced for estimation of leaf area and its twin concept of leaf area index (LAI; e.g. see [1][2][3][4][5][6][7][8][9][10][11]), the destructive approaches have remained as the most accurate [12] and the direct method of leaf area measurement. Indeed, even the parameters of the non-destructive techniques are calibrated or validated based on the destructive methods, which may be a laborious practice.…”

Drones provide spatial and volumetric data to deliver new insights into microclimate modelling

“…While ground-based techniques such as the use of hemispherical photography (Zhao et al 2019) or specialised scientific instrumentation such as the LiCOR LAI-2000 (Calders et al 2018), can potentially be used to measure this heterogeneity, they are limited in their spatial extent, and in their ability to capture spatially explicit variation. Drone platforms offer an exciting though unproven means by which to bridge the gap between in situ measurement, and wider spatial coverage, compared to informative structural information provided by satellite data (Fig.…”

Accelerating leaf area measurement using a volumetric approach

“…Although at the present, various non-destructive techniques and tools have been introduced for estimation of leaf area and its twin concept of leaf area index (LAI; e.g., see [ 7 – 17 ]), the destructive approaches have remained as the most accurate [ 18 ] and the direct method of leaf area measurement. Indeed, even the parameters of the non-destructive techniques are calibrated or validated based on the destructive methods, which may be a laborious practice.…”