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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Canadell J, Riba M, Andrés P (1988) Biomass equations for Quercus Ilex L. in the Montseny Massif, Northeastern Spain. Forestry 61: 137–147
Carvalho JP, Parresol BR (2003) Additivity in tree biomass components of Pyrenean oak (Quercus pyrenaica Willd). For Ecol Manage 179: 269–276
Chapell R (1989) Fitting bent lines to data, with applications to allometry. J Theo Biol 138: 235–256
Cunia T (1979) On tree biomass tables and regression: some statistical comments. In: Frayer WE (ed) Forest resource inventory workshop proceedings. Colorado State University, Fort Collins
Currie ID, Durbán M (2002) Flexible smoothing with P-splines: a unified approach. Stat Modell 4: 333–349
Deans JD, Moran J, Grace J (1996) Biomass relationships for tree species in regenerating semi-deciduous tropical moist forest in Cameroon. For Ecol Manage 88: 215–225
De Boor C (1978) A practical guide to splines. Springer, Berlin
Eilers PHC (1999) Comment on “The analysis of designed experiments and longitudinal data by using smoothing splines”, by Verbyla AP, Cullis BR, Kenward MG, Welham JS. Appl Stat 48: 269–311
Eilers PHC, Marx BD (1996) Flexible smoothing with B-splines and penalties. Stat Sci 11: 89–1216
Eilers PHC, Currie ID, Durbán M (2006) Fast and compact smoothing on large multidimensional grids. Comput Stat Data Anal 50: 61–76
Foresna (2007) 07 Internacional, Proyecto Forsee, Foresna-Zurgaia, http://www.foresna.org/es/servicios/forsee/
Gutiérrez R, Gutiérrez-Sánchez R, Nafidi A (2008) Emissions of greenhouse gases attributable to the activities of the land transport: modelling and analysis using I-CIR stochastic diffusion. The case of Spain. Environmetrics 19: 137–161
Hashimoto T, Tange T, Masumori M, Yagui H, Sakaki S, Kojima K (2004) Allometric equations for pioneer tree species and estimation of aboveground biomass of a tropical secondary forest in East Kalimantan. Tropics 14: 123–130
IFN2, Villaescusa R, Daz R (1998) Segundo Inventario Forestal Nacional (1986–1996) Ministerio de Medio Ambiente, ICONA, Madrid
Jacobs MW, Cunia T (1980) Use of dummy variables to harmonize tree biomass tables. Can J For Res 10: 483–490
Ketterings QM, Coe R, van Noordwijk M, Ambafau Y, Palm CA (2001) Reducing uncertainty in the use of allometric biomass equations for predicting above-ground tree biomass in mixed secondary forests. For Ecol Manage 146: 199–209
Kurz WA, Beukema SJ, Apps MJ (1996) Estimation of root biomass and dynamics for the carbon budget model of the Canadian forest sector. Can J For Res 26: 1973–1979
Loetsch F, Zhrer F, Haller KE (1973) Forest inventory. BLV Verlagsgesellschaft, München
Mehtätalo L, Gregoire TG, Burkhart HE (2008) Comparing strategies for modeling tree diameter percentiles from remeasured plots. Environmetrics 19: 529–548
Muggeo V (2003) Estimating regression models with unknown break-points. Stat Med 22: 3055–3071
Muggeo V (2004) Segmented: segmented relationships in regression models. R package version 0.1-4
Parresol BR (1999) Assessing tree and stand biomass: a review with examples and critical comparisons. For Sci 13: 573–593
Parresol BR (2001) Additivity of nonlinear biomass equations. Can J For Res 31: 865–878
Pinheiro J, Bates D (2000) Mixed-effects models in S and S-PLUS. Springer, New York
Pinheiro J, Bates D, DebRoy S (2008) The R core team, nlme: linear and nonlinear mixed effects models. R package version 3.1-89
Reed DD, Llechty HO, Jones EA, Zhang Y (1996) Above and belowground dry matter accumulation pattern derived from dimensional biomass relationships. For Sci 42: 236–241
Ruppert D (2002) Selecting the number of knots for penalized splines. J Comput Graph Stat 11: 735–757
Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric regression. Cambridge University Press, New York
Sas Institute Inc (2004) SAS/STATR 9
Segura M (2005) Allometric models for tree volume and total aboveground biomass in a tropical humid forest in Costa Rica. Biotropica 37: 2–8
Srivastava VK, Giles DEA (1987) Seemingly unrelated regression equations models. Marcel Dekker, New York
Ugarte MD, Goicoa T, Militino AF, Durbán M (2009) Spline smoothing in small area trend estimation and forecasting. Comput Stat Data Anal 53: 3616–3629
Vann DR, Palmiotto PA, Strimbeck GR (1998) Allometric equations for two South America conifers: test of a non-destructive method. For Ecol Manage 106: 55–71
Wand MP (2003) Smoothing and mixed models. Comput Stat 18: 223–249
Wood SN (2003) Thin plate splines regression. J R Stat Soc B 65: 95–114
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Goicoa, T., Militino, A.F. & Ugarte, M.D. Modelling aboveground tree biomass while achieving the additivity property. Environ Ecol Stat 18, 367–384 (2011). https://doi.org/10.1007/s10651-010-0137-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10651-010-0137-9