CROBAS (Mäkelä 1997, Valentine and Mäkelä 2005) is a generic tree growth model that can be applied to different stand structures, e.g., mean tree per species, size classes or age classes. Growth in CROBAS is based on carbon acquisition and allocation and is calculated using an annual time resolution. The model describes individual trees in terms of 13 variables (Table), including biomass variables and crown, stem, and root system dimensions. Growth is assumed to follow from net annual photosynthesis, which is growth photosynthesis minus growth and maintenance respiration. Total growth is allocated to the different biomass components. The allocation is performed to maintain a number of structural rules.

Because of the structural rules and simple geometry, 12 of the 13 state variables are bound together through linear or allometric equations in balanced growth (for treatment of disturbances to balanced growth, see Mäkelä 1999). Because of its key role in production, foliage mass (Wf) is used as a representative variable of the mutually related variables. The variable not bound to the rest is the length of the bare bole (Hs), the development of which is largely controlled by the local environment of the tree and cannot therefore be derived from a tree balance only. Crown rise is mainly determined by stand density and crown coverage in CROBAS. Detailed descriptions are given in Mäkelä (1997)Valentine and Mäkelä (2005) and Mäkelä and Valentine (2020).

Description of CROBAS model.


Table. Tree structure variables used in CROBAS.

Tree structure variables used in CROBAS model.



Mäkelä, A. and Sievänen, R. (1992). Height growth strategies in open-grown trees. Journal of Theoretical Biology 159, 443-467.

Mäkelä, A.  (1997) A carbon balance model of growth and self-pruning in trees based on structural relationships.  Forest Science 43(1):7-24

Mäkelä, A. (1999). Acclimation in dynamic models based on structural relationships. Functional Ecology 13:145-156.
Valentine H.T. and Mäkelä A 2005. Bridging process-based and empirical approaches to modeling tree growth. Tree Physiology 25:769–779

Duursma, R.A., Mäkelä, A., Reid, D.E.B., Jokela, E.J., Porté, A., Roberts, S.D. 2010. Self-shading affects allometric scaling  in trees. Functional Ecology 24:723-730.

Mäkelä A, Valentine H.T. 2020. Models of tree and stand dynamics. Theory, formulation and application. Springer Nature Switzerland AG. Cham, Switzerland. 310 pp.