Additivity of nonlinear tree crown width models: Aggregated and disaggregated model structures using nonlinear simultaneous equations

Accurate quantification of tree biomass is critical and essential for calculating carbon storage, as well as for studying climate change, forest health, forest productivity, nutrient cycling, etc. Tree biomass is typically estimated using statistical models. Although various biomass models have been developed thus far, most of them lack a detailed investigation of the additivity properties of biomass components and inherent correlations among the components and aboveground biomass. This study compared the nonadditive and additive biomass models for larch (Larix olgensis Henry) trees in Northeast China. For the nonadditive models, the base model (BM) and mixed effects model (MEM) separately fit the aboveground and component biomass, and they ignore the inherent correlation between the aboveground and component biomass of the same tree sample. For the additive models, two aggregated model systems with one (AMS1) and no constraints (AMS2) and two disaggregated model systems without (DMS1) and with an aboveground biomass model (DMS2) were fitted simultaneously by weighted nonlinear seemingly unrelated regression (NSUR) and applied to ensure additivity properties. Following this, the six biomass modeling approaches were compared to improve the prediction accuracy of these models. The results showed that the MEM with random effects had better model fitting and performance than the BM, AMS1, AMS2, DMS1, and DMS2; however, when no subsample was available to calculate random effects, AMS1, AMS2, DMS1, and DMS2 could be recommended. There was no single biomass modeling approach to predict biomass that was best for all aboveground and component biomass except for MEM. The overall ranking of models based on the fit and validation statistics obeyed the following order: MEM > DMS1 > AMS2 > AMS1> DMS2 > BM. This article emphasized more on the methodologies and it was expected that the methods could be applied by other researchers to develop similar systems of the biomass models for other species, and to verify the differences between the aggregated and disaggregated model systems. Overall, all biomass models in this study have the benefit of being able to predict aboveground and component biomass for larch trees and to be used to predict biomass of larch plantations in Northeast China.

Section: Parameter Estimation Methodsmentioning

confidence: 99%

Comparison of Tree Biomass Modeling Approaches for Larch (Larix olgensis Henry) Trees in Northeast China

Dong

Zhang

et al. 2020

“…According to the biomass allocation analysis, the biomass of leaves and pods accounted for 2.22% and 1.82% of the total biomass, respectively-therefore, for a relatively small proportion. To improve the fitting performance of the crown biomass model, some studies have added crown height, crown width, and crown length as additional predictors into the allometric growth equation or biomass additive system, which significantly improved the fitting and performance [33,60]. In future research, crown height, crown width, and crown length could be added into the additive system of biomass equations to improve the accuracy of the crown biomass model.…”

Section: Verification and Application Of Biomass Additivity Systemmentioning

confidence: 99%

Developing Additive Systems of Biomass Equations for Robinia pseudoacacia L. in the Region of Loess Plateau of Western Shanxi Province, China

Cui

Liu

et al. 2020

The accurate estimation of forest biomass is important to evaluate the structure and function of forest ecosystems, estimate carbon sinks in forests, and study matter cycle, energy flow, and the effects of climate change on forest ecosystems. Biomass additivity is a desirable characteristic to predict each component and the total biomass since it ensures consistency between the sum of the predicted values of components such as roots, stems, leaves, pods, and branches and the prediction for the total tree. In this study, 45 Robinia pseudoacacia L. trees were harvested to determine each component and the total biomass in the Loess Plateau of western Shanxi Province, China. Three additive systems of biomass equations of R. pseudoacacia L., based on the diameter at breast height (D) only and on the combination of D and tree height (H) with D2H and DbHc, were established. To ensure biomass model additivity, the additive system of biomass equations considers the correlation among different components using simultaneous equations and establishes constraints on the parameters of the equation. Seemingly uncorrelated regression (SUR) was used to estimate the parameters of the additive system of biomass equations, and the jackknifing technique was used to verify the accuracy of prediction of the additive system of biomass equations. The results showed that (1) the stem biomass contributed the most to the total biomass, comprising 51.82% of the total biomass, followed by the root biomass (24.63%) and by the pod and leaf biomass, which accounted for the smallest share, comprising 1.82% and 2.22%, respectively; (2) the three additive systems of biomass equations of R. pseudoacacia L. fit well with the models and were effective at making predictions, particularly for the root, stem, above-ground, and total biomass (R2adj > 0.812; root mean square error (RMSE) < 0.151). The mean absolute error (MAE) was less than 0.124, and the mean prediction error (MPE) was less than 0.037. (3) When the biomass model added the tree height predictor, the goodness of fit R2adj increased, RMSE decreased, and the accuracy of prediction was much improved. In particular, the additive system, which was developed based on DbHc combination prediction factors, was the most accurate. The additive system of biomass equations established in this study can provide a reliable and accurate estimation of the individual biomass of R. pseudoacacia L. in the Loess region of western Shanxi Province, China.

“…To date, additivity has been used in the forestry field, for calculations such as biomass, volume [12,13,32], and crown [10,11]. However, it is rare to study the additivity of taper equation.…”

Section: Discussionmentioning

confidence: 99%

“…Previously, model researchers usually considered the dob, dib or bark thickness separately, and often neglected the inherent correlations among them, even if the accuracy of a single model was very high. Recently, many scholars have solved the additive problem by constructing additive models in forestry, such as additive volume, biomass or crown width equations [8][9][10][11][12][13]. In this study, we used the stem taper function to construct additive models for dob, dib and bark thickness.…”

Section: Introductionmentioning

confidence: 99%

A Newly Built Model of an Additive Stem Taper System with Total Disaggregation Model Structure for Dahurian Larch in Northeast China

Jiang

Shahzad

2021

Stem taper function is an important concept in forest growth and yield modeling, and forest management. However, the additivity of the function and the inherent correlations between stem components (diameter outside bark—dob, diameter inside bark—dib, and double-bark thickness—dbt) are seldom considered. In this paper, a total disaggregation model (TDM) structure was developed based on the well-known Kozak (2004) model to ensure the additivity of the stem components. The reconstructed model was fitted with the data of 1281 felled Dahurian larch trees from three regions of Daxing’anling Mountains in Northeast China. The results from TDM were compared with other additive model structures including adjustment in proportion (AP), non-additive taper models (NAM), and three logical structures of NSUR (AMO, SMI, SMB). The results showed that the difference was significant among the three regions. The performance of TDM was slightly better than those of other model structures. Therefore, TDM was considered as another optimal additive system to estimate stem, bark thickness, and volume predicting for Dahurian larch in Northeast China besides NSUR, a method widely used in calculating additive volume or biomass throughout the world. We believe this work is cutting-edge, and that this methodology can be applied to other tree species.