Abstract
Accurate estimation of tree biomass is required for accounting for and monitoring forest carbon stocking. Allometric biomass equations constructed by classical statistical methods are widely used to predict tree biomass in forest ecosystems. In this study, a Bayesian approach was proposed and applied to develop two additive biomass model systems: one with tree diameter at breast height as the only predictor and the other with both tree diameter and total height as the predictors for planted Korean larch (Larix olgensis Henry) in the Northeast, P.R. China. The seemingly unrelated regression (SUR) was used to fit the simultaneous equations of four tree components (i.e., stem, branch, foliage, and root). The model parameters were estimated by feasible generalized least squares (FGLS) and Bayesian methods using either non-informative priors or informative priors. The results showed that adding tree height to the model systems improved the model fitting and performance for the stem, branch, and foliage biomass models, but much less for the root biomass models. The Bayesian methods on the SUR models produced narrower 95% prediction intervals than did the classical FGLS method, indicating higher computing efficiency and more stable model predictions, especially for small sample sizes. Furthermore, the Bayesian methods with informative priors performed better (smaller values of deviance information criterion (DIC)) than those with the non-informative priors. Therefore, our results demonstrated the advantages of applying the Bayesian methods on the SUR biomass models, not only obtaining better model fitting and predictions, but also offering the assessment and evaluation of the uncertainties for constructing and updating tree biomass models.
Highlights
In the practice of sustainable forest management, tree biomass is primarily used to calculate the carbon storage and sequestration of forests and further to comprehend climate change and forest health, productivity, and nutrient cycling [1,2]
We investigated the impacts of five priors of model parameters on the model fitting and validation results: (1) direct Monte Carlo simulation with Jeffreys invariant prior (DMC); (2) Gibbs sampler using Jeffreys invariant prior (Gs-J); and (3) Gibbs sampler using three priors of multivariate normal distribution, i.e., artificial setting (Gs-MN), self-sampling estimate (Gs-MN1), and other research results on biomass models (Gs-MN2), respectively
For the Bayesian methods Gs-MN1 on both SURM1 and SURM2, the prior information consisted of the model parameter values estimated by the feasible generalized least squares (FGLS) method with subsample sizes of 10%, 20%, 30%, . . . , and 90% of the 174 trees sampled without replacement
Summary
In the practice of sustainable forest management, tree biomass is primarily used to calculate the carbon storage and sequestration of forests and further to comprehend climate change and forest health, productivity, and nutrient cycling [1,2]. Hundreds of biomass equations have been developed for different tree species around the world [5,6,7]. Tree diameter at breast height (DBH) is the commonly used predictor variable, which is considered the readily attainable and most reliable sole predictor [8]. Tree height (H) is used for developing biomass models to Forests 2020, 11, 1302; doi:10.3390/f11121302 www.mdpi.com/journal/forests. The biomass models with both DBH and H are recognized more stable and reliable for predicting tree biomass [11,12]. Various modeling approaches have been explored and applied for developing tree biomass models [13,14]
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