A hierarchical framework for incorporating tree scale uncertainty into national foliage biomass estimates
Allometric models are routinely used to estimate biomass at the individual tree scale, with the goal of using these estimates to calculate carbon stocks within national forest inventories. However, owing to a lack of comprehensive felled tree datasets for even common tree species, these models may be highly uncertain, and this error is frequently ignored when scaling biomass estimates up to the national scale. Here, we present a Bayesian hierarchical modeling framework for predicting foliage biomass and propagating resulting uncertainty into national stock estimates with the US Forest Service Forest Inventory and Analysis (FIA) data. We take advantage of a large, multispecies felled tree database to compare several foliage biomass models, and to quantify resulting uncertainty when applied to observations within FIA. To compare models, we both assessed model fit to the felled tree data, and performed Bayesian posterior predictive checks by simulating new datasets from the posterior predictive distribution. Specific objectives are: (1) compare the fit of linear and component ratio models to felled tree data; (2) assess performance of general, multispecies biomass models relative to species-specific equations; and (3) quantify the contribution of error in tree-scale allometric models to the overall uncertainty of national forest biomass estimates.
Results reveal that linear models which directly estimate foliage biomass provide a better fit than component ratio models, which estimate total aboveground biomass and foliar ratio. We found that species-specific models better reproduced the distribution of the observed data than general multi-species models, equating to an average reduction in root mean squared error of 19-26 percent in our posterior predictive checks. However, even in this best case scenario, our hierarchical model resulted in large prediction uncertainties (>50 percent relative to predicted means) when applied to the FIA data. Uncertainty was higher for larger trees, owing to a bias towards small individuals within our data, and was larger for conifers than for hardwood species. The large error from our predictive models suggests that empirical estimation of foliage biomass with general biomass equations may ignore significant uncertainty when applied to estimate national biomass stocks. The hierarchical model framework we present provides an approach for propagating this uncertainty during biomass estimation, and rising availability of felled tree datasets makes fitting these models possible. While we focus on foliage biomass, a particularly dynamic pool, our proposed framework and uncertainty estimates provide an important benchmark for the estimation of all live tree biomass pools.