Integrating regional climate change into allometric equations for estimating tree aboveground biomass of Masson pine in China

  • Liyong Fu
  • Xiangdong Lei
  • Zongda Hu
  • Weisheng Zeng
  • Shouzheng Tang
  • Peter Marshall
  • Lin Cao
  • Xinyu Song
  • Li Yu
  • Jingjing Liang
Original Paper


Key message

A climate-sensitive aboveground biomass (AGB) equation, in combination with nonlinear mixed-effects modeling and dummy variable approach, was developed to examine how climate change may affect the allometric relationships between tree diameter and biomass. We showed that such changes in allometry need to be taken into account for estimating tree AGB in Masson pine.


As a native species and being widely distributed in subtropical China, Masson pine (Pinus massoniana Lamb.) forests play a pivotal role in maintaining forest ecosystem functions and mitigation of carbon concentration increase at the atmosphere. Traditional biomass allometric equations do not account for a potential effect of climate on the diameter–biomass relationships. The amplitude of such an effect remains poorly documented.


We presented a novel method for detecting the long-term (2041–2080) effects of climate change on the diameter–biomass relationships and the potential consequences for long-term changes of biomass accumulation for Masson pine.


Our approach was based on a climate-sensitive AGB model developed using a combined nonlinear mixed-effects model and dummy variable approach. Various climate-related variables were evaluated for their contributions to model improvement. Heteroscedasticity was accounted for by three residual variance functions: exponential function, power function, and constant plus function.


The results showed that diameter at breast height, together with the long-term average of growing season temperature, total growing season precipitation, mean temperature of wettest quarter, and precipitation of wettest quarter, had significant effects on values of AGB. Excessive rain during the growing season and high mean temperature in the wettest quarter reduced the AGB, while a warm growing season and abundant precipitation in the wettest quarter increased the AGB.


Climate change significantly affected the allometric scale of biomass equation. The new climate-sensitive allometric model developed in this study may improve biomass predictions compared with the traditional model without climate effects. Our findings suggested that the AGB of Masson pine trees with the same diameter at breast height under three climate scenarios including representative concentration pathway (RCP) 2.6, RCP 4.5, and RCP 8.5 in the future period 2041–2080 would increase by 24.8 ± 32.7% (mean ± standard deviation), 27.0 ± 33.4%, and 27.7 ± 33.8% compared with the constant climate (1950–2000), respectively. As a consequence, we may expect a significant regional variability and uncertainty in biomass estimates under climate change.


Masson pine Subtropical China Climate change Climate-sensitive aboveground biomass model Nonlinear mixed-effects model Dummy variable approach 



The article was funded by the Forestry Public Welfare Scientific Research Project (No. 201504303) and the Chinese National Natural Science Foundation (Nos. 31470641, 31300534, and 31570628). We appreciate the valuable comments from the chief editor Dr. Erwin Dreyer, Dr. Jean-Michel Leban, the handling editor, and two anonymous reviewers who improved the manuscript.

Compliance with ethical standards

The biomass data used in this study were collected according to the protocol of data collection for tree biomass modeling which was drafted by the State Forestry Administration of China (SFA 2014).

Supplementary material

13595_2017_636_MOESM1_ESM.docx (17 kb)
ESM 1 (DOCX 16 kb)


  1. Anitha K, Verchot LV, Joseph S, Herold M, Manuri S, Avitabile V (2015) A review of forest and tree plantation biomass equations in Indonesia. Ann Forest Sci 72(8):981–997CrossRefGoogle Scholar
  2. Ashraf MI, Meng F-R, Bourque CP-A, MacLean DA (2015) A novel modelling approach for predicting forest growth and yield under climate change. PLoS One 10(7):e0132066. doi: 10.1371/journal.pone.0132066 CrossRefPubMedPubMedCentralGoogle Scholar
  3. Boisvert-Marsh L, Périé C, de Blois S (2014) Shifting with climate? Evidence for recent changes in tree species distribution at high latitudes. Ecosphere 5:1–33CrossRefGoogle Scholar
  4. Chave J, Andalo C, Brown S, Cairns MA, Chambers JQ, Eamus D, Folster H, Fromard F, Higuchi N, Kira T, Lescure JP, Nelson BW, Ogawa H, Puig H, Riera B, Yamakura T (2005) Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 145:87–99CrossRefPubMedGoogle Scholar
  5. Chave J, Réjou-Méchainn M, Burquez A, Chidumayo E, Colgan MS, Delitti Welington BC et al (2014) Improved allometric models to estimate the aboveground biomass of tropical trees. Glob Chang Biol 20(10):3177–3190CrossRefPubMedGoogle Scholar
  6. Ciais P, Reichstein M, Viovy N, Granier A, Ogee J, Allard V, Aubinet M, Buchmann N, Bernhofer C, Carrara A (2005) Europe-wide reduction in primary productivity caused by the heat and drought in 2003. Nature 437:529–533CrossRefPubMedGoogle Scholar
  7. Daniels LD, Veblen TT (2004) Spatiotemporal influences of climate on altitudinal tree line in northern Patagonia. Ecology 85:1284–1296CrossRefGoogle Scholar
  8. Davidian M, Giltinan DM (1995) Nonlinear models for repeated measurement data. Chapman and Hall, New YorkGoogle Scholar
  9. Deng X, Zhang L, Lei P, Xiang W, Yan W (2014) Variations of wood basic density with tree age and social classes in the axial direction within Pinus massoniana stems in Southern China. Ann Forest Sci 71(4):505–516CrossRefGoogle Scholar
  10. Diéguez-Aranda U, Burkhart HE, Amateis RL (2006) Dynamic site model for loblolly pine (Pinus taeda L.) plantations in the United States. For Sci 52:262–272Google Scholar
  11. Eggers J, Lindner M, Zudin S, Zaehle S, Liski J (2008) Impact of changing wood demand, climate and land use on European forest resources and carbon stocks during the 21st century. Glob Chang Biol 14:2288–2303CrossRefGoogle Scholar
  12. Emmingham WH, Waring RH (1977) An index of photosynthesis for comparing forest sites in western Oregon. Can J For Res 7:165–174CrossRefGoogle Scholar
  13. Feng X, Cheng R, Xiao W, Wang R, Wang X, Cao B (2011) Effects of air temperature in growth season on Masson pine (Pinus massoniana) radial growth in north subtropical region of China. Chin J Ecol 30:650–655 (In Chinese with English abstract) Google Scholar
  14. Fu L, Zeng W, Zhang H, Wang G, Lei Y, Tang S (2014a) Generic linear mixed-effects individual-tree biomass models for Pinus massoniana Lamb. in Southern China. South Forests 76(1):47–56CrossRefGoogle Scholar
  15. Fu L, Wang M, Lei Y, Tang S (2014b) Parameter estimation of two-level nonlinear mixed effects models using first order conditional linearization and the EM algorithm. Comput Stat Data An 69:173–183CrossRefGoogle Scholar
  16. Fu L, Lei Y, Wang G, Bi H, Tang S, Song X (2016) Comparison of seemingly unrelated regressions with multivariate errors-in-variables models for developing a system of nonlinear additive biomass equations. Trees 30:839–857CrossRefGoogle Scholar
  17. Gao X, Shi Y, Zhang D, Giorgi F (2012) Climate change in China in the 21st century as simulated by a high resolution regional climate model. Chin Sci Bull 57:1188–1195 (In Chinese with English abstract) CrossRefGoogle Scholar
  18. Gholz HL (1982) Environmental limits on aboveground net primary production, leaf area, and biomass in vegetation zones of the Pacific Northwest. Ecology 63:469–481CrossRefGoogle Scholar
  19. Hamann A, Wang T (2006) Potential effects of climate change on ecosystem and tree species distribution in British Columbia. Ecology 87:2773–2786CrossRefPubMedGoogle Scholar
  20. Hijmans RJ, Cameron SE, Parra JL, Jones PG, Jarvis A (2005) Very high resolution interpolated climate surfaces for global land areas. Int J Climatol 25:1965–1978CrossRefGoogle Scholar
  21. Hsu JS, Powell J, Adler PB (2012) Sensitivity of mean annual primary production to precipitation. Glob Chang Biol 18:2246–2255CrossRefGoogle Scholar
  22. Huang B (1992) On the boundary of tropics in China: I. Definition of tropical and subtropical zones in internation. Sci Geogr Sin 12:97–104 (In Chinese with English abstract) Google Scholar
  23. Intergovernmental Panel on Climate Change (IPPC) (2001) Climate change 2001. Synthesis report. In: Watson RT, Albritton DL, Baker T, Bashmakov IA, Canziani O, Christ R (eds) A contribution of Working Groups I, II, and III to the Third Assessment Report of Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, p 398ppGoogle Scholar
  24. IPCC (2013) Summary for policy-makers. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM (eds) Climate change 2013: the physical Science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge and New York, NYGoogle Scholar
  25. Jiang H, Radtke PJ, Weiskittel AR, Coulston JW, Guertin PJ (2015) Climate- and soil-based models of site productivity in eastern US tree species. Can J For Res 45:325–342CrossRefGoogle Scholar
  26. Keith H, Mackey BG, Lindenmayer DB (2009) Re-evaluation of forest biomass carbon stocks and lessons from the world’s most carbon-dense forests. PNAS 106:11635–11640CrossRefPubMedPubMedCentralGoogle Scholar
  27. Landsberg JJ, Sands P (2011) Physiological ecology of forest production: principles, processes and models. Academic Press, LondonGoogle Scholar
  28. Lei X, Yu L, Hong L (2016) Climate-sensitive integrated stand growth model (CS-ISGM) of Changbai larch (Larix olgensis) plantations. For Ecol Manag 376:265–275CrossRefGoogle Scholar
  29. Lin D, Lai J, Muller-Landau HC, Mi X, Ma K (2012) Topographic variation in aboveground biomass in a subtropical evergreen broad-leaved forest in China. PLoS One 7:e48244. doi: 10.1371/journal.pone.004824 CrossRefPubMedPubMedCentralGoogle Scholar
  30. Marlon JR, Bartlein PJ, Carcaillet C, Gavin DG, Harrison SP, Higuera PE (2008) Climate and human influences on global biomass burning over the past two millennia. Nature 1:697–702Google Scholar
  31. Medlyn BE, Duursma RA, Zeppel MJ (2011) Forest productivity under climate change: a checklist for evaluating model studies. WIRES Climate Change 2:332–355CrossRefGoogle Scholar
  32. Monleon VJ, Lintz HE (2015) Evidence of tree species’ range shifts in a complex landscape. PLoS One 10:e0118069. doi: 10.1371/journal.pone.0118069 CrossRefPubMedPubMedCentralGoogle Scholar
  33. Peng C, Ma Z, Lei X, Zhu Q, Chen H, Wang W, Liu S, Li W, Fang X, Zhou X (2011) A drought-induced pervasive increase in tree mortality across Canada’s boreal forests. Nat Clim Chang 1:467–471CrossRefGoogle Scholar
  34. Pickett S (1989) Space-for-time substitution as an alternative to long-term studies. In: Likens GE (ed) Long-term studies in ecology: approaches and alternatives. Springer, New York, pp 110–135CrossRefGoogle Scholar
  35. Pinheiro JC, Bates DM (2000) Mixed-effects models in S and S-PLUS. Springer-Verlag, New York, NYCrossRefGoogle Scholar
  36. Poudel BC, Sathre R, Gustavsson L, Bergh J, Lundström A, Hyvönen R (2011) Effects of climate change on biomass production and substitution in north-central Sweden. Biomass Bioenergy 35:4340–4355CrossRefGoogle Scholar
  37. R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna Available at: (accessed 4 September 2011)Google Scholar
  38. Schuur EAG (2003) Productivity and global climate revisited: the sensitivity of tropical forest growth to precipitation. Ecology 84:1165–1170CrossRefGoogle Scholar
  39. SFA (State Forestry Administration) (2012) China’s forestry 2006–2010. China Forestry Publishing House, Beijing (In Chinese) Google Scholar
  40. SFA (State Forestry Administration) (2014) Technical regulation on sample collections for tree biomass modeling. Standards Press of China, Beijing (In Chinese) Google Scholar
  41. Shuman JK, Shugart HH (2009) Evaluating the sensitivity of Eurasian forest biomass to climate change using a dynamic vegetation model. Environ Res Lett 4:1–7CrossRefGoogle Scholar
  42. Sinervo B, Méndez-de-la-Cruz F, Miles DB (2010) Erosion of lizard diversity by climate change and altered thermal niches. Science 328:894–899CrossRefPubMedGoogle Scholar
  43. Stegen J, Swenson N, Enquist B, White E, Phillips O, Jorgensen P, Weiser M, Mendoza AM, Vargas PN (2011) Variation in above-ground forest biomass across broad climatic gradients. Glob Ecol Biogeogr 20:744–754CrossRefGoogle Scholar
  44. Strömgren M, Linder S (2002) Effects of nutrition and soil warming on stemwood production of a boreal Norway spruce stand. Glob Chang Biol 8:1195–1204CrossRefGoogle Scholar
  45. Subedi N, Sharma M (2013) Climate-diameter growth relationships of black spruce and jack pine trees in boreal Ontario, Canada. Glob Chang Biol 19:505–516CrossRefPubMedGoogle Scholar
  46. Tardif J, Flannigan M, Bergeron Y (2001) An analysis of the daily radial activity of 7 boreal tree species, northwestern Quebec. Environ Monit Assess 67:141–160CrossRefPubMedGoogle Scholar
  47. Tian X, Sohngen B, Kim JB, Ohrel S, Cole J (2016) Global climate change impacts on forests and markets. Environ Res Lett 11:035011CrossRefGoogle Scholar
  48. Trincado G, Burkhart HE (2006) A generalized approach for modeling and localizing stem profile curves. For Sci 52:670–682Google Scholar
  49. Vieilledent G, Vaudy R, Andriamanohisoa SFD, Rakotonarivo OS, Randrianasolo HZ et al (2012) A universal approach to estimate biomass and carbon stock in tropical forests using generic allometric models. Ecol Appl 22(2):572–583CrossRefPubMedGoogle Scholar
  50. West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122–126CrossRefPubMedGoogle Scholar
  51. West GB, Brown JH, Enquist BJ (1999) A general model for the structure and allometry of plant vascular systems. Nature 400:664–667CrossRefGoogle Scholar
  52. Wilmking M, Juday GP, Barber VA, Zald HSJ (2004) Recent climate warming forces contrasting growth responses of white spruce at treeline in Alaska through temperature thresholds. Glob Chang Biol 10:1724–1736CrossRefGoogle Scholar
  53. Wykoff WR (1990) A basal area increment model for individual conifers in the northern Rocky Mountains. For Sci 36:1077–1110Google Scholar
  54. Xia B, Lan T, He S (1996) Nonlinear response function of growth of Pinus massoniana to climate. Chin J Plant Ecol 20(1):51–56Google Scholar
  55. Xiang W, Liu S, Deng X, Shen A, Lei X, Tian D, Zhao M, Peng C (2011) General allometric equations and biomass allocation of Pinus massoniana trees on a regional scale in southern China. Ecol Res 26:697–711CrossRefGoogle Scholar
  56. Yang Q, Zheng D, Wu S (2006) On subtropical zone of China. J Subtrop Res Environ 1:1–10 (In Chinese with English abstract) Google Scholar
  57. Zeng WS, Zhang HR, Tang SZ (2011) Using the dummy variable model approach to construct compatible single-tree biomass equations at different scales-a case study for Masson pine (Pinus massoniana) in southern China. Can J For Res 41:1547–1554CrossRefGoogle Scholar
  58. Zeng W, Duo H, Lei X, Chen X, Wang X, Pu Y, Zou W (2017) Individual tree biomass equations and growth models sensitive to climate variables for Larix spp. in China. Eur J Forest Res. doi: 10.1007/s10342-017-1024-9 Google Scholar
  59. Zhang L, Deng X, Lei X, Xiang W, Peng C, Lei P, Yan W (2012) Determining stem biomass of Pinus massoniana L. through variations in basic density. Forestry 85(5):601–609CrossRefGoogle Scholar
  60. Zhang L, Deng X, Lei X, Zhao Z, Xiang W, Yan W (2013) Pinus massoniana productivity at different age stages in relation to climatic factors. Chin J Ecol 32:1104–1110 (In Chinese with English abstract) Google Scholar

Copyright information

© INRA and Springer-Verlag France 2017

Authors and Affiliations

  • Liyong Fu
    • 1
  • Xiangdong Lei
    • 1
  • Zongda Hu
    • 2
  • Weisheng Zeng
    • 3
  • Shouzheng Tang
    • 1
  • Peter Marshall
    • 4
  • Lin Cao
    • 5
  • Xinyu Song
    • 1
    • 6
  • Li Yu
    • 1
  • Jingjing Liang
    • 7
  1. 1.Research Institute of Forest Resource Information TechniquesChinese Academy of ForestryBeijingPeople’s Republic of China
  2. 2.College of ResourcesSichuan Agricultural UniversityChengduPeople’s Republic of China
  3. 3.Academy of Forest Inventory and PlanningState Forestry AdministrationBeijingPeople’s Republic of China
  4. 4.Department of Forest Resources ManagementUniversity of British ColumbiaVancouverCanada
  5. 5.Co-Innovation Center for Sustainable Forestry in Southern ChinaNanjing Forestry UniversityNanjingPeople’s Republic of China
  6. 6.College of Computer and Information TechniquesXinyang Normal UniversityXinyangPeople’s Republic of China
  7. 7.Division of Forestry and Natural ResourcesWest Virginia UniversityMorgantownUSA

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