Variability and uncertainty in forest biomass estimates from the tree to landscape scale: the role of allometric equations

Abstract

Biomass maps are valuable tools for estimating forest carbon and forest planning. Individual-tree biomass estimates made using allometric equations are the foundation for these maps, yet the potentially-high uncertainty and bias associated with individual-tree estimates is commonly ignored in biomass map error. We developed allometric equations for lodgepole pine (Pinus contorta), ponderosa pine (P. ponderosa), and Douglas-fir (Pseudotsuga menziesii) in northern Colorado. Plot-level biomass estimates were combined with Landsat imagery and geomorphometric and climate layers to map aboveground tree biomass. We compared biomass estimates for individual trees, plots, and at the landscape-scale using our locally-developed allometric equations, nationwide equations applied across the U.S., and the Forest Inventory and Analysis Component Ratio Method (FIA-CRM). Total biomass map uncertainty was calculated by propagating errors from allometric equations and remote sensing model predictions. Two evaluation methods for the allometric equations were compared in the error propagation—errors calculated from the equation fit (equation-derived) and errors from an independent dataset of destructively-sampled trees (n?=?285).

Tree-scale error and bias of allometric equations varied dramatically between species, but local equations were generally most accurate. Depending on allometric equation and evaluation method, allometric uncertainty contributed 30–75% of total uncertainty, while remote sensing model prediction uncertainty contributed 25–70%. When using equation-derived allometric error, local equations had the lowest total uncertainty (root mean square error percent of the mean [% RMSE]?=?50%). This is likely due to low-sample size (10–20 trees sampled per species) allometric equations and evaluation not representing true variability in tree growth forms. When independently evaluated, allometric uncertainty outsized remote sensing model prediction uncertainty. Biomass across the 1.56 million ha study area and uncertainties were similar for local (2.1 billion Mg;?% RMSE?=?97%) and nationwide (2.2 billion Mg; ?% RMSE?=?94%) equations, while FIA-CRM estimates were lower and more uncertain (1.5 billion Mg; ?% RMSE?=?165%).

Allometric equations should be selected carefully since they drive substantial differences in bias and uncertainty. Biomass quantification efforts should consider contributions of allometric uncertainty to total uncertainty, at a minimum, and independently evaluate allometric equations when suitable data are available.