Modelling aboveground tree biomass while achieving the additivity property

Abstract

Measuring forest tree biomass is becoming a very important issue due to the general environmental awareness motivated by global warming and climate change. However, weighing a tree is a very complicated, expensive, and destructive process. The tree is divided into several parts, and the total weight is obtained by adding the weight of the different components. The biomass information of a forest is obtained using statistical models, but one of the main difficulties is that the additivity property is not generally satisfied, i.e., when adding the predicted weights for the different tree components, the result does not match up with the total weight predicted for the tree. In this work, alternative methods for obtaining biomass predictions satisfying the additivity property are analyzed. In particular, segmented regression models with a common break point and penalized splines with the same smoothing parameter achieve the additivity property without any further adjustments. Some classical models will be also used for comparison purposes. Results are illustrated with real data from a beech forest (European project FORSEE-020) in the province of Navarre, Spain.

Live above- and belowground biomass of a Mozambican evergreen forest: a comparison of estimates based on regression equations and biomass expansion factors

“…To ensure the additivity of minor component biomass estimates into major components and whole tree biomass estimates, minor component, major component and whole tree biomass models were fitted using the same regressors (Parresol 1999;Goicoa et al 2011). For this, first the best tree component and whole tree biomass regression equations were selected by running various possible linear regressions on combinations of the independent variables (DBH, tree height) and evaluating them using the following goodness of fit statistics: coefficient of determination (R 2 ), standard deviation of residuals (S y.x ), mean residual (MR), and graphical analysis of residuals.…”

“…The mean residual and the standard deviation of residuals were expressed as relative values, hereafter referred to as percent mean residual (MR (%)) and coefficient of variation of residuals (CV r (%)), respectively, which are more revealing. The computation and interpretation of these fit statistics were previously described by Mayer (1941), Gadow & Hui (1999), Ruiz-Peinado et al (2011), andGoicoa et al (2011).…”

“…Linear models were preferred over nonlinear models because the procedure of enforcing additivity by using the same regressors is only applicable for linear models (Parresol 1999;Goicoa et al 2011) and because the procedure of combining the error of the first and second sampling phases in double sampling (Cunia 1986a) is limited to biomass regressions estimated by linear weighted least squares (Cunia 1986a).…”

Biomass Modelling ofAndrostachys johnsoniiPrain: A Comparison of Three Methods to Enforce Additivity

“…The estimation of aboveground biomass is important to predict the amount of carbon that is sequestered [3][4][5], to assess nutrient cycling and fluxes and energy wood potentials [4,6], and to provide estimates for the different tree components [5]. These types of estimates are important for several reasons as follows: (i) stem wood biomass is an important quantity because this component is the only one used in the forest industry, and the carbon therefore remains stored for a long time and is not released into the atmosphere; (ii) in many species, branches and foliage are left in the forest and decompose, releasing CO 2 and nutrients; (iii) in some species, especially broadleaf species, the branches are collected by members of local communities for use as firewood, which will result in release of CO 2 ; 2 International Journal of Forestry Research (iv) the stump and root system are left in the forest, allowing the stump to either sprout (regrow), continuing the sequestration process, or decompose along with the roots, releasing CO 2 and nutrients; and (v) in some tree species, belowground biomass can account for more than one-third of the total biomass [7].…”

“…This feature is called additivity. Various authors, such as Goicoa et al [5], Kozak [8], Cunia [9], Cunia and Briggs [10,11], Jacobs and Cunia [12], Parresol [4,13], and Carvalho and Parresol [14], have proposed and/or discussed various methods to ensure the property of additivity.…”