A Mathematical Model for Estimating Carbon Storage Dynamics of Forest Communities

Using the JABOWA single-tree growth model, a program was designed to estimate carbon storage dynamics in the aboveground biomass of a mixed forest community. The developed model incorporates the parameters of tree species that are common to the forests of Central Russia: pedunculate oak ( Quercus robur L.), silver birch ( Betula pendula Roth), common aspen ( Populus tremula L.), small-leaved lime ( Tilia cordata Mill.), Scots pine ( Pinus sylvestris L.), Norway spruce ( Picea abies (L.) H. Karst.), and fir ( Abies Mill.). A differential equation for tree diameter at breast height ( D ) was solved. The results were compared with the forest inventory data. The amount of carbon stored in the aboveground biomass of trees was calculated following the methodology suggested by the Intergovernmental Panel on Climate Change. The dynamics of tree volume were analyzed. An analytical formula was proposed to describe the dependence of tree volume and stored carbon on tree age. The differences in the rates of tree volume growth and carbon accumulation were identified among the species studied. The analytical and numerical results on stored carbon and tree age showed a good agreement for a test plot with the known species composition and tree count, which is located within the forest part of the carbon polygon of Kazan Federal University. The formula offers an accurate estimation and prediction of carbon storage dynamics in mixed forest communities with trees varying in age and, hence, is a valuable tool for managing forestry activities. However, when predicting tree biomass growth and carbon storage dynamics, one should also consider forest site quality classes reflecting the actual growth conditions of trees. Developing a mathematical model based on forest site quality classes as a key variable would help increase the reliability of biomass growth and carbon storage predictions for forest communities. Notably, the obtained model applies to actual forest communities with known species composition and fails to account for natural regeneration. To incorporate this parameter, spatial diffusion models that describe forest regeneration in non-forest areas should be utilized.