Regression estimators for aboveground biomass and its constituent parts of trees in native southern Brazilian forests

Abstract The mathematical models used applying the Nonlinear Seemingly Unrelated Regressions (NSUR) or Weighted Nonlinear Seemingly Unrelated Regressions (WNSUR) methodologies can contribute to generate acceptable and reliable estimates of total aboveground biomass and its constituent parts, which are needed to implement forest management strategies to maintain desirable and sustainable carbon stocks. The aim of this study was: 1) to fit the sample data with independent nonlinear regression models and present the results obtained from the respective statistical estimates for total biomass aboveground and the constituent parts of trees in native forest trees. 2) To fit the sample data with regression models simultaneously, that is, whose models are composed of appropriate combinations of their coefficients, in order to obtain additivity of the estimates and present better results for the total aboveground biomass and the constituent parts of the trees. 3) To apply weighting procedures to the variances of the fitted models. 4) To evaluate the error due to the regression function on forest biomass estimation. The data came from eight sites located in the states of Parana and Rio Grande do Sul, Brazil, and information was collected on diameter at 1.30 m aboveground (DBH), total height, biomasses of the trunk components (branches and leaves) and total aboveground biomass. Non-linear functions were independently and simultaneously fitted, using DBH and total height as independent variables in the regression models. Independent fitting of equations was performed using generalized nonlinear least squares (ENGLS) and simultaneous fitting of equations was obtained by means of NSUR. Weighting, by applying a variance structure in the two procedures, was done to solve the issue of heteroscedasticity. Numerically, the equations fitted simultaneously performed better and were more efficient than the independently fitted models, which resulted in biological inconsistency, that is, non-additivity of the biomass of constituent parts of the trees and the total biomass. Simultaneous fitting generated superior statistical and biological properties to obtain tree estimates of the of constituent parts of the trees and total aboveground biomass in native forests of southern Brazil. The smaller error due to the regression function used in the forest biomass inventory was obtained by simultaneous fitting. With these results, the procedure using simultaneous and weighted fitting of equations (WNSUR) is recommended to fit biomass equations for native forests in southern Brazil.

[1]  J. Stape,et al.  Köppen's climate classification map for Brazil , 2013 .

[2]  James H. Torrie,et al.  Principles and procedures of statistics: a biometrical approach (2nd ed) , 1980 .

[3]  B. Parresol.  Assessing Tree and Stand Biomass: A Review with Examples and Critical Comparisons , 1999, Forest Science.

[4]  G. Tonoli,et al.  Effect of natural weathering and accelerated artificial in physical, mechanical and colorimetric OSB panels. , 2017 .

[5]  David L. R. Affleck,et al.  Critical analyses when modeling tree biomass to ensure additivity of its components. , 2018, Anais da Academia Brasileira de Ciencias.

[6]  R. Teskey,et al.  Additive tree biomass equations for Betula platyphylla Suk. plantations in Northeast China , 2018, Annals of Forest Science.

[7]  B. Nelson,et al.  Improved allometric models to estimate the aboveground biomass of tropical trees , 2014, Global change biology.

[8]  R. Mather,et al.  Sampling trees to develop allometric biomass models: How does tree selection affect model prediction accuracy and precision? , 2020 .

[9]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[10]  David L. R. Affleck,et al.  Additive nonlinear biomass equations: A likelihood-based approach , 2016 .

[11]  George Z. Gertner,et al.  The sensitivity of measurement error in stand volume estimation , 1990 .

[12]  H. Akaike.  A new look at the statistical model identification , 1974 .

[13]  Matieu Henry,et al.  Manual for building tree volume and biomass allometric equations: from field measurement to prediction , 2012 .

[14]  C. Sanquetta,et al.  Simultaneous estimation as alternative to independent modeling of tree biomass , 2015, Annals of Forest Science.

[15]  James K. Brown.  Weight and density of crowns of Rocky Mountain conifers , 1978 .

[16]  Michael L. Clutter,et al.  Additive Tree Biomass Equations for Midrotation Loblolly Pine Plantations , 2015 .

[17]  R. Ferreira,et al.  Predicting of biomass in Brazilian tropical dry forest: a statistical evaluation of generic equations. , 2017, Anais da Academia Brasileira de Ciencias.

[18]  Benjamin M. Bolker,et al.  Ecological Models and Data in R , 2008 .

[19]  C. Pérez-Cruzado,et al.  Improving biomass estimation in a Populus short rotation coppice plantation , 2017 .

[20]  Sylvio Péllico Netto,et al.  Additivity of tree biomass components using ratio estimate. , 2019, Anais da Academia Brasileira de Ciencias.

[21]  H. Temesgen,et al.  Aboveground biomass equations for evergreen broadleaf forests in South Central Coastal ecoregion of Viet Nam: Selection of eco-regional or pantropical models , 2016 .

[22]  Jonathan William Trautenmüller,et al.  MODELLING OF ALLOMETRIC EQUATIONS FOR BIOMASS ESTIMATE IN DECIDUOUS FOREST , 2018, FLORESTA.

[23]  Bernard R. Parresol,et al.  Additivity of nonlinear biomass equations , 2001 .

[24]  Y. Xiong,et al.  An improved approach to estimate above-ground volume and biomass of desert shrub communities based on UAV RGB images , 2021, Ecological Indicators.

[25]  Michael B Kane,et al.  New Variable-Top Merchantable Volume and Weight Equations Derived Directly from Cumulative Relative Profiles for Loblolly Pine , 2017 .

[26]  Eric H. Wharton,et al.  Estimating tree biomass regressions and their error, proceedings of the workshop on tree biomass regression functions and their contribution to the error , 1987 .

[27]  Xiaoli Zhang,et al.  Estimation of tree height and aboveground biomass of coniferous forests in North China using stereo ZY-3, multispectral Sentinel-2, and DEM data , 2021, Ecological Indicators.

[28]  R. Briggs,et al.  Forcing additivity of biomass tables: some empirical results , 1984 .

[29]  Jonathan William Trautenmüller,et al.  Vertical distribution of aboveground biomass in a Seasonal Deciduous Forest. , 2017 .

[30]  F. Schumacher.  Logarithmic expression of timber-tree volume , 1933 .

[31]  H. Temesgen,et al.  Methods for estimating aboveground biomass and its components for Douglas-fir and lodgepole pine trees , 2016 .

[32]  H. Temesgen,et al.  Allometric Equations for Estimating Tree Aboveground Biomass in Tropical Dipterocarp Forests of Vietnam , 2016 .

[33]  Francis Hallé,et al.  Arquitectura de los árboles , 2010 .

[34]  Xiangtong Lei,et al.  How large is the difference in large-scale forest biomass estimations based on new climate-modified stand biomass models? , 2021, Ecological Indicators.

[35]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[36]  E. Cienciala,et al.  Biomass functions applicable to Scots pine , 2006, Trees.

[37]  Jonathan William Trautenmüller,et al.  PATH ANALYSIS APPLIED TO EVALUATION OF BIOMASS ESTIMATES IN SUBTROPICAL FORESTS AT BRAZIL , 2019, FLORESTA.

[38]  S. Syampungani,et al.  Species-specific allometric models for estimation of the above-ground carbon stock in miombo woodlands of Copperbelt Province of Zambia , 2018 .

[39]  Richard Condit,et al.  Error propagation and scaling for tropical forest biomass estimates. , 2004, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[40]  A. Sebbenn,et al.  Genetic variation and parameters in an open-pollinated progeny test of Peltophorum dubium (Sprengel) Taubert, in Luiz Antonio - SP. , 2012 .