Research Article: A critique of general allometry-inspired models for estimating forest carbon density from airborne LiDAR

Date Published: April 19, 2019

Publisher: Public Library of Science

Author(s): Rebecca A. Spriggs, Mark C. Vanderwel, Trevor A. Jones, John P. Caspersen, David A. Coomes, Qi Chen.


There is currently much interest in developing general approaches for mapping forest aboveground carbon density using structural information contained in airborne LiDAR data. The most widely utilized model in tropical forests assumes that aboveground carbon density is a compound power function of top of canopy height (a metric easily derived from LiDAR), basal area and wood density. Here we derive the model in terms of the geometry of individual tree crowns within forest stands, showing how scaling exponents in the aboveground carbon density model arise from the height−diameter (H−D) and projected crown area−diameter (C−D) allometries of individual trees. We show that a power function relationship emerges when the C−D scaling exponent is close to 2, or when tree diameters follow a Weibull distribution (or other specific distributions) and are invariant across the landscape. In addition, basal area must be closely correlated with canopy height for the approach to work. The efficacy of the model was explored for a managed uneven−aged temperate forest in Ontario, Canada within which stands dominated by sugar maple (Acer saccharum Marsh.) and mixed stands were identified. A much poorer goodness−of−fit was obtained than previously reported for tropical forests (R2 = 0.29 vs. about 0.83). Explanations for the poor predictive power on the model include: (1) basal area was only weakly correlated with top canopy height; (2) tree size distributions varied considerably across the landscape; (3) the allometry exponents are affected by variation in species composition arising from timber management and soil conditions; and (4) the C-D allometric power function was far from 2 (1.28). We conclude that landscape heterogeneity in forest structure and tree allometry reduces the accuracy of general power-function models for predicting aboveground carbon density in managed forests. More studies in different forest types are needed to understand the situations in which power functions of LiDAR height are appropriate for modelling forest carbon stocks.

Partial Text

Aboveground carbon density (ACD) is an important forest property to map in the context of the global carbon cycle [1–3]. Classically, ACD has been estimated using tree size measurements recorded from networks of forest plots, with generalised or species−specific allometries used to convert field measures of diameter and height into tree biomass estimates, and then into ACD estimates [4, 5]. More recently, methods using remote sensing technologies have been developed to complement these plot networks: airborne or spaceborne LiDAR sensors have proven to be particularly effective for estimating ACD because they provide detailed information about forest structure, which is in turn closely related to ACD [6].

Deriving the AM−GM from individual tree measurements has revealed the origins of its parameters, the assumptions behind the power function formula, and the situations in which it is unlikely to make accurate predictions. Below, we explore specific explanations for low goodness−of−fit, including that (1) the basal area and wood density of plots are not closely correlated with top canopy height or gap fraction as measured by LiDAR; (2) tree size distributions are not conserved across the landscape; and (3) the exponents of the allometries are affected by systematic changes in species composition, and the exponent of the crown area allometry deviates from 2. Our findings suggest that among−stand variability in structure and composition are key factors in determining the accuracy of the AM−GM.

The allometry-inspired AM-GM model appears to predict forest carbon more reliably in tropical forests than in temperate ones. Asner and Mascaro [8] achieved a goodness−of−fit of R2 = 0.83 compared with R2 = 0.18 in this study, even though the models were identical (Table 2). Their RMSE was 9% of the mean ACD compares with 23% for our models (Fig 3). Duncanson et al. [14] also observed poor model performance when testing the AM−GM in two out of three temperate forest sites in the USA (R2 = 0.13, 0.18 and 0.73).