Carbon Balance

  • Annikki Mäkelä
  • Harry T. Valentine


This chapter introduces the basic carbon-balance approach for trees, when considered over their lifetime, at an annual (or growing-season) resolution. At this scale, the key issues of model development include: (1) realistic long-term dynamic properties, (2) responses of growth and mortality of competing individuals, and (3) responses to eco-physiological inputs.

Supplementary material


  1. Ågren GI (1983) Nitrogen productivity of some conifers. Can J For Res 13:494–500CrossRefGoogle Scholar
  2. Ågren GI, Franklin O (2003) Root:shoot ratios, optimization and nitrogen productivity. Ann Bot 92:795–800CrossRefGoogle Scholar
  3. de Wit CT (1978) Simulation of assimilation, respiration and transpiration of crops. Pudoc, WageningenGoogle Scholar
  4. Duursma RA, Mäkelä A (2007) Summary models for light interception and light-use efficiency of non-homogeneous canopies. Tree Physiol 27:859–870CrossRefGoogle Scholar
  5. Duursma RA, Mäkelä A, Reid DEB, Jokela EJ, Porté A, Roberts SD (2010) Branching networks in gymnosperm trees: implications for metabolic scaling. Funct Ecol 24:723–730CrossRefGoogle Scholar
  6. Grace JC (1990) Modeling the interception of solar radiant energy and net photosynthesis. In: Dixon RK, Meldahl RS, Ruark GA, Warren WG (eds) Process modeling of forest growth responses to environmental stress. Timber Press, Portland, pp 142–158Google Scholar
  7. Guillemot J, Martin-StPaul NK, Dufrêne E, François C, Soudani K, Ourcival JM, Delpierre N (2015) The dynamic of the annual carbon allocation to wood in European tree species is consistent with a combined source-sink limitation of growth: implications for modelling. Biogeosciences 12:2773–2790CrossRefGoogle Scholar
  8. Hubbard RM, Bond BJ, Ryan MG (1999) Evidence that hydraulic conductance limits photosynthesis in old Pinus ponderosa trees. Tree Physiol 19:165–172CrossRefGoogle Scholar
  9. Ingestad T (1980) Growth, nutrition and nitrogen fixation in grey alder at varied rate of nitrogen addition. Physiol Plant 50:353–364CrossRefGoogle Scholar
  10. Ingestad T, Ågren GI (1992) Theories and methods on plant nutrition and growth. Physiol Plant 84:177–184CrossRefGoogle Scholar
  11. Ingestad T, Aronsson A, Ågren GI (1981) Nutrient flux density model of mineral nutrition in conifer ecosystems. Studia Forestalia Suecica 160:61–72Google Scholar
  12. Kira T, Shidei T (1967) Primary production and turnover of organic matter in different forest ecosystems of the Western Pacific. Jap J Ecol 17:70–87Google Scholar
  13. Landsberg JJ (1986) Physiological ecology of forest production. Academic Press, LondonGoogle Scholar
  14. Landsberg JJ, Waring RH (1997) A generalised model of forest productivity using simplified concepts of radiation use efficiency, carbon balance and partitioning. For Ecol Manage 95: 209–228CrossRefGoogle Scholar
  15. Lang ARG (1991) Application of some of Cauchy’s theorems to the estimation of surface areas of leaves, needles and branches of plants, and light transmittance. Agric For Meteorol 55:191–212CrossRefGoogle Scholar
  16. Ludlow AR, Randle TJ, Grace JC (1990) Developing a process-based growth model for Sitka spruce. In: Dixon RK, Meldahl RS, Ruark GA, Warren WG (eds) Process modeling of forest growth responses to environmental stress. Timber Press, Portland, pp 249–262Google Scholar
  17. Luenberger DG (1979) Introduction to dynamic systems. John Wiley & Sons, New YorkGoogle Scholar
  18. Mäkelä A (1997) A carbon balance model of growth and self-pruning in trees based on structural relationships. For Sci 43:239–267Google Scholar
  19. Mäkelä A, Valentine HT (2001) The ratio of NPP to GPP: evidence of change over the course of stand development. Tree Physiol 21:1015–1030CrossRefGoogle Scholar
  20. Mäkelä A, Landsberg J, Ek AR, Burk TE, Ter-Mikaelian M, Ågren GI, Oliver CD, Puttonen P (2000) Process-based models for forest ecosystem management: current state of the art and challenges for practical implementation. Tree Physiol 20:289–298CrossRefGoogle Scholar
  21. McMurtrie RE (1991) Relationship of forest productivity to nutrient and carbon supply: a modeling analysis. Tree Physiol 9:87–99CrossRefGoogle Scholar
  22. McMurtrie R, Wolf L (1983) Above- and below-ground growth of forest stands: a carbon budget model. Ann Bot 52(4):437–448CrossRefGoogle Scholar
  23. Monsi M, Saeki T (1953) Uber den lichtfaktor in den pflanzengesellschaften und seine bedeutung fur die stoffproduktion. Jap J Bot 14:22–52Google Scholar
  24. Nilson T (1999) Inversion of gap frequency data in forest stands. Agric For Meteorol 98/99: 437–448CrossRefGoogle Scholar
  25. Oker-Blom P, Pukkala T, Kuuluvainen T (1989) Relationship between radiation interception and photosynthesis in forest canopies: effect of stand structure and latitude. Ecol Modell 49:73–87CrossRefGoogle Scholar
  26. Penning de Vries FWT (1975) Use of assimilates in higher plants. In: Cooper JP (ed) Photosynthesis and productivity in different environments, Cambridge University Press, Cambridge, pp 459–480Google Scholar
  27. Pruyn ML, Gartner BL, Harmon ME (2002) Within-stem variation of respiration in Pseudotsuga menziesii (Douglas-fir) trees. New Phytol 154:359–372CrossRefGoogle Scholar
  28. Pruyn ML, Gartner BL, Harmon ME (2005) Storage versus substrate limitation to bole respiratory potential in two coniferous tree species of contrasting sapwood width. J Exp Bot 56:2637–2649CrossRefGoogle Scholar
  29. Ryan MG (1991) A simple method for estimating gross carbon budgets for vegetation in forest ecosystems. Tree Physiol 9:255–266CrossRefGoogle Scholar
  30. Ryan MG (1995) Foliar maintenance respiration of subalpine and boreal trees and shrubs in relation to nitrogen content. Plant Cell Environ 18:765–772CrossRefGoogle Scholar
  31. Sala A, Hoch G (2009) Height-related growth declines in ponderosa pine are not due to carbon limitation. Plant Cell Environ 32:22–30CrossRefGoogle Scholar
  32. Sprugel DG (1990) Components of woody-tissue respiration in young Abies amabilis (Dougl.) Forbes trees. Trees 4:88–99CrossRefGoogle Scholar
  33. Thornley JHM (1972) A model to describe the partitioning of photosynthate during vegetative plant growth. Ann Bot 36:419–430CrossRefGoogle Scholar
  34. Thornley JHM (1976) Mathematical models in plant physiology. Academic Press, LondonGoogle Scholar
  35. Thornley JHM, Johnson IR (1990) Plant and crop modelling. Clarendon Press, OxfordGoogle Scholar
  36. Vanninen P, Mäkelä A (2000) Needle and stem wood production in Scots pine (Pinus sylvestris) trees of different age, size and competitive status. Tree Physiol 20:527–533CrossRefGoogle Scholar
  37. Yoder BJ, Ryan MG, Waring RH, Schoettle AW, Kaufmann MR (1994) Evidence of reduced photosynthetic rates in old trees. For Sci 40:513–527Google Scholar

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Authors and Affiliations

  • Annikki Mäkelä
    • 1
  • Harry T. Valentine
    • 2
  1. 1.Department of Forest SciencesUniversity of HelsinkiHelsinkiFinland
  2. 2.USDA Forest ServiceNorthern Research StationDurhamUSA

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