Photosynthesis is the driver of forest growth and carbon sequestration. Trees assimilate carbon dioxide from the atmosphere, convert it to sugars and use it to build leaves, roots and wood. The photosynthesis process is well known and unique in its universal character: all plant forms (apart from C4 plants!) seem to have adopted the same process over the course of evolution. Because of this, photosynthesis models, deriving photosynthesis from environmental driving variables and vegetation leaf area, are quite generally applicable to different species and vegetation zones.
Carbon allocation is the process that determines how photosynthates are distributed between respiration and the growth of different tree organs. The loss of carbon in respiration reflects the use of energy in building new structures as well as maintaining their vitality. Part of the growth is used to replace the shedding of leaves and fine roots. As a result of natural selection, the different vital organs grow to conserve a tree structure that best serves the tree’s needs of acquiring resources and withstanding physical forces in the environment the tree is growing in. For example, in poor soils trees allocate more growth to roots than in fertile soils, and in open environments exposed to winds their trunks taper more than in the shelter of dense stands. This has led to environment-dependent regularities in structure that can be used to estimate carbon allocation with models.
The PREBAS model utilises these simple biological principles to calculate the dynamics of tree and forest growth and related carbon sequestration. It includes both trees and ground vegation, and it has been linked with the soil carbon model Yasso that converts the leaf, root and woody litter of the forest into soil carbon and microbial respiration. The model system thus estimates forest ecosystem carbon fluxes and how they accumulate over time into forest carbon stocks, and how this depends on weather conditions and forest management.
Parameters of a process-based model, such as PREBAS, ideally are constants defined in relation to the biological processes or tree structure described by the model. These have been estimated in measurements or experiments on the basis of their biological definition. In principle, these type of parameters are fundamentally different from parameters in an empirical model that often have no other meaning but that expressed through a statistical fit. However, since any process-based model is a simplification, and because some of the parameters cannot easily be measured based on their definition, the independent parameter estimates always contain an element of error, or uncertainty. That’s why they are represented by an interval – or sometimes by a probability distribution – rather than just one fixed value. However, all these uncertainties combine in the model and propagate to model outputs which, as a result, may deviate considerably from corresponding measurements. Advanced mathematical model-data fusion methods are then used to solve the parameterization challenge.
Bayesian calibration is an advanced statistical method of model-data fusion that allows us to fine-tune the estimated model parameter set – termed the prior distribution – such that the model predictions are in the best possible agreement with data on the predicted variables. The resulting fine-tuned parameters are called the posterior distribution. The advantage of the method is that it allows for all kinds of data to be utilised: the data does not need to cover all cases, different types of data sets can be combined, and even expert opinion can be taken into account. If the prior parameters are very uncertain and the data set on model outputs has high coverage of variables and situations concerned, the method starts to resemble statistical fitting. In practice, Bayesian calibration allows us simultaneously to utilise the theory-based and often streamlined structure of process models on one hand, and the high fidelity with data of empirical models on the other hand (Figure 1).
PREBAS has been quite extensively calibrated in past research, using ecosystem carbon exchange data from eddy covariance stations and forestry data from Finnish permanent forest growth experiments conducted by Luke. In HIKET we further improve the calibration by incorporating National Forest Inventory data from permanent inventory sample plots.
In the HIKET project, PREBAS is just one of the models used for estimating the temporal development of the carbon budget of Finnish forests. Comparisons with other models will be carried out by simulating the past development of growth and carbon sequestration in Finland, and future simulations will be conducted using different climate change scenarios. In this way we try, in HIKET, to gain an idea of prediction uncertainties that are due to our poor understanding of the system. If all models based on different principles and calculation methods converge to the same result, this increases our confidence in the outcomes. In the opposite case, we acknowledge that the results are still uncertain, and hopefully the analysis gives us some directions for improvement.
Figure 1. Schematic presentation of theory-based modelling process and its interaction with data. The model is developed based on existing theoretical and empirically acquired knowledge. The model is developed based on existing theoretical and empirically acquired knowledge. Model parameters are estimated from observations based on their definition. A dynamic simulation starts from an initial state that has been measured – for example, the size and density of trees in a stand. Model predictions are tested against measured values of the output variables, and model-data fusion methods utilise these to improve the parameter estimates.
Literature
Minunno F, Peltoniemi M, Launiainen S, Aurela M, Mammarella I, Lindroth A, Lohela A, Minkkinen K, Mäkelä A 2016. Calibration and validation of a semi-empirical flux ecosystem model for coniferous forests in the Boreal region. Ecological Modelling 341:37-52.
Minunno F., Peltoniemi M., Härkönen S., Kalliokoski T., Mäkinen H., Mäkelä A. 2019. Bayesian calibration of a carbon balance model PREBAS using data from permanent growth experiments and national forest inventory. Forest Ecology and Management 440: 208-257.
Mäkelä, A., Minunno, F., Kujala, H., Kosenius, A.K., Heikkinen, R.K., Junttila, V., Peltoniemi, M., Forsius, M. 2023. Effect of forest management choices on carbon sequestration and biodiversity at national scale. AMBIO 52:1737-1756.
Junttila, V., Minunno, F., Peltoniemi, M., Forsius, M., Akujaervi, A., Ojanen, P., Maekelae, A. 2023. Quantification of forest carbon flux and stock uncertainties under climate change and their use in regionally explicit decision making: Case study in Finland. AMBIO 52:1716-1733.