Minimizing Bias in Biomass Allometry: Model Selection and Log-Transformation of Data (original) (raw)
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CAPITALIZING ON THE INFORMATION IN ALLOMETRIC EQUATION DATA BASES FOR FOREST BIOMASS ESTIMATION
In many countries, inventory data or biomass or volume equations are often incomplete or unavailable. Either taxonomic information is not accurate at the species level, or else no literature exist compiling particular allometric equations for some species. On the other hand, some species are represented by many alternative equations in the database. The vast quantity of information that allometric equation databases such as Globallometree can provide, can be capitalized to inform other, non-available species from the ranges and distributions of aboveground biomass estimates that other, better known species provide. In this study we provide an alternative method that takes those elements to estimate overall plot aboveground biomass from bootstrapping different equations belonging to a certain ecozone. Using a real inventory plot as an example, we prove that such estimates present error levels similar to those of generalized pantropical equations when a minimum set of rules for quality control has been added. This opens the possibility to establish more adequate quality control protocols that end up providing even better estimates than those published pantropical equations.
Towards a functional and simplified allometry for estimating forest biomass
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Aboveground tree biomass (M) can be estimated using a power function in the form of M = aD b where a and b are the scaling coefficient and scaling exponent, respectively, and D the tree breast-height diameter. Both a and b are reported to vary with species, site and age. However West et al. [West, G.B., Brown, J.H., Enquist, B.J., 1999. A general model for the structure and allometry of plant vascular systems. Nature 400, 664-667] suggested that M should scale against D with a universal exponent (b = 8/3), because the scaling exponent would depend on an optimal tree architecture. Moreover a should be related with the wood density (r) [Enquist, B.J., West, G.B., Charnov, E.L., Brown, J.H., 1999. Allometric scaling of production and life-history variation in vascular plants. Nature 401, 907-911].
Forests
Effective initiatives for forest-based mitigation of climate change rely on continuous efforts to improve the estimation of forest biomass. Allometric biomass models, which are nonlinear models that predict aboveground biomass (AGB) as a function of diameter at breast height (D) and tree height (H), are typically used in forest biomass estimations. A combined variable D2H may be used instead of two separate predictors. The Q-ratio (i.e., the ratio between the parameter estimates of D and parameter estimates of H, in a separate variable model) was proposed recently as a measure to guide the decision on whether D and H can be safely combined into D2H, being shown that the two model forms are similar when Q = 2.0. Here, using five European beech (Fagus sylvatica L.) biomass datasets (of different Q-ratios ranging from 1.50 to 5.05) and an inventory dataset for the same species, we investigated the effects of combining the variables in allometric models on biomass estimation over large ...
Modelling of Allometric Equations for Biomass Estimate in Deciduous Forest
FLORESTA, 2018
This paper aimed to test and adjust allometric models to estimate biomass in a Deciduous Forest. The data were obtained from seven 12 x 12 m plots, from which 91 trees were cut down. Only trees with diameter at breast height (DBH) greater than 5 cm were measured, and the fitting of the models was performed based on the DBH, total height (H) and total dry biomass (DAB) for each individual tree. The adjusted equations with no stratification presented adjusted determination coefficients (R 2 aj) ranging from 0.726 to 0.972 and standard errors in percentage (Syx%) from 33.5 to 119.6. The best adjusted model for nonstratified dataset was obtained by the Stepwise procedure, leading to the equation: DAB = β0 + β1.(DBH 3) + β2.H + β3.(DBH 3 .H), with 0.954 of R 2 aj and 44.0 of Syx%. For stratified dataset, only the diameter class higher than 15 cm presented acceptable results, with 0.968 of R 2 aj and 26.5 of Syx%. The current database has shown good quality measurements for fitting stochastic models to estimate the biomass of each tree.
On simplifying allometric analyses of forest biomass
Forest Ecology and Management, 2004
Tree biomass plays a key role in sustainable management and in estimating forest carbon stocks. The most common mathematical model in biomass studies takes the form of the power function M=aDb where a and b are the allometric coefficients to be determined by empirical data, and M the total aboveground tree dry biomass for a specific diameter at breast height, D.In this study the development and comparison of three methods for simplifying allometric equations of aboveground biomass estimation are reported. Based on the criterion of the relative difference (RD) between observed and predicted biomass data, the small trees sampling scheme (SSS) predicted quite accurate estimates for raw data reported in 10 studies. The SSS equation was based on the hypothesis that information provided in published allometric equations, in conjunction with two pairs of empirical M–D values, are enough to obtain reliable predictions for aboveground stand biomass. In addition, predictions of M based on theoretical values of b were also tested with the RD criterion, but reliability of predictions in 10 studies is questioned. Finally, fractal geometry was used to develop a ‘reductionist’ model for M estimation and implications from its implementation in biomass studies are discussed. We totally based our investigation on a metadata set derived from published aboveground biomass allometric studies conducted for different species spanning the globe.
South African Journal of Science, 2011
The need for accurate quantification of the amount of carbon stored in the environment has never been greater. Carbon sequestration has become a vital component of the battle against global climate change, and monitoring and quantifying this process are major challenges for policymakers. Plant allometric equations allow managers and scientists to quantify the biomass contained in a tree without cutting it down, and therefore can play a pivotal role in measuring carbon sequestration in forests and savannahs. These equations have been available since the beginning of the 20th century, but their usefulness depends on the ability to estimate the error associated with the equations -something which has received scant attention in the past. This paper provides a method based on the theory of linear regression and the lognormal distribution to derive confidence limits for estimates of biomass derived from plant allometric equations. Allometric equations for several southern African savannah species are provided, as well as the parameters and equations required to calculate the confidence intervals. This method was applied to data collected from a sampling campaign carried out in a savannah landscape at the Skukuza flux site, Kruger National Park, South Africa. Here the error was 10% of the total site biomass for the woody biomass and 2% for the leaf biomass. When the data were split into individual plots and used to estimate site biomass (as would occur in most sampling schemes) the error increased to 16% and 12% of the woody and leaf biomasses, respectively, as the sampling errors were added to the errors in the allometric equation. These methods can be used in any discipline that applies allometric equations, such as health sciences and animal physiology.
Ecological Indicators, 2020
Developing allometric biomass models is an important process because reliability of forest biomass and carbon estimations largely depend on the accuracy and precision of such models. The effects of tree sampling on tree aboveground biomass (AGB) prediction accuracy and precision are complex and can, therefore, be difficult to quantify. In this paper we use a Monte Carlo simulation to investigate how model prediction accuracy and precision are affected by tree sampling approaches. Because diameter at breast height (D, in cm) is the most common predictor of tree AGB (in kg dry weight), we focused our analysis on the AGB-D relationship. The following sample characteristics were investigated: (i) sample size; (ii) extent of the D-range (difference between the largest and the smallest D value); (iii) position of D-range (characterized by the starting point of D-range); and (iv) the size-distribution (distribution of D) of sample trees. We found that, although the natural variability of AGB-D relationship was a key driver for both prediction accuracy and precision, the above sample characteristics were important for improving prediction accuracy. Although having a negligible effect on precision, both sample size and size-distribution of sample trees, greatly influenced prediction accuracy. We demonstrate that selecting a constant number of trees for each D class (i.e. uniform distribution of the sample trees over the Drange) generally produced models that were more accurate predictors of AGB. The extent and position of Drange, although considerably affecting the goodness of fit and the standard errors of allometric model parameters, had only a marginal effect on AGB prediction accuracy and precision. Furthermore, we showed that R 2 was a poor indicator of model prediction accuracy and precision, due to its sensitivity to changes in D-range. These findings inform certain practical recommendations we report for improving the accuracy and precision of biomass prediction.
Forest Ecology and Management, 2001
Estimates of forest biomass are needed for tracking changes in C stocks, as well as for other purposes. A common method for estimating forest biomass is through use of allometric equations which relate the biomass of individual trees to easily obtainable non-destructive measurements, such as diameter. A common form is BaD b for biomass B, diameter D and parameters a and b. Field data collected in Sumatra and compared with previously published data show that the values of a and b vary between sites. This variation is likely to be the major source of uncertainty if biomass estimates are produced using equations that are not calibrated for individual sites. However, calibration by collection of B and D data for each site is unrealistic, requiring destructive measures. Methods of choosing values for a and b are, therefore, proposed that do not require destructive measurements. The parameter b can be estimated from the site-speci®c relationship between height (H) and diameter, HkD c as b2c. The parameter a can be estimated from the average wood density (r) at the site as arr, where r is expected to be relatively stable across sites. The allometric equation proposed is therefore BrrD 2c . #
Reducing the error in biomass estimates strongly depends on model selection
Annals of Forest Science, 2014
Key message Improving the precision of forest biomass estimates requires prioritizing the different sources of errors. In a tropical moist forest in central Africa, the choice of the allometric equation was found to be the main source of error. • Context When estimating the forest biomass at the landscape level using forest inventory data and allometric models, there is a chain of propagation of errors including the measurement errors, the models' prediction error, the error due to the model choice, and the sampling error.
Allometric regressions for improved estimate of secondary forest biomass in the central Amazon
Forest Ecology and Management, 1999
Estimates of the sequestering of carbon by secondary forests ± which occupy almost half the deforested area of the Brazilian Amazon ± will be improved by the use of accurate allometric relationships for non-destructive measurement of standing biomass and by an evaluation of the suitability of existing equations for application in secondary forest. Species-speci®c and mixed-species regressions for estimating total above-ground dry weight (DW) were therefore developed using eight abundant secondary forest tree species in the central Amazon. Using only DBH as the input variable, the species-speci®c equations estimated DW of individual trees with an average error of 10±15%. For the mixed-species equations, developed using 132 trees from seven of the eight species (excluding Cecropia), average error in estimating DW of individual trees was 19.8% using only DBH and 15.0% using DBH plus speci®c density of the wood (SD). Average SD for each species can be substituted without increasing the error of the estimate. Adding total tree height (H) as an input variable provided only a slight reduction in error to 14.0%. Previously published mixed-species biomass regression models, based on primary and secondary forest trees of the Amazon, were also cross-validated against the trees of this study. Two of these models, based on primary forest plots and using only DBH as an input, overestimated biomass by 10±60% for central Amazonian secondary forest trees in the size range 5±25 cm. The overestimate was greatest for the larger trees. Including Cecropia in the test group will make the overestimate even greater. Those published equations using DBH, H and SD as inputs, whether from secondary or primary forest plots, showed better agreement with the sample-derived regressions and lower average errors in estimation of individual tree dry weights. #