Simulation of biomass in individual tree growth models adds a level of complexity to the modelling steps described above. A seamless integration of biomass models in the simulation environment is required and one of the major objectives is to project biomass consistently with other outputs like volume. This means, for example, that simulated stem biomass should be consistent with the product of simulated stem volume and wood density. The application of allometric equations to estimate biomass from diameter and height usually leads to inconsistencies with taper and volume models as far as stem biomass is concerned. The reason is that biomass models are naturally parameterised on much smaller data sets because of the huge effort it takes to gather biomass data. In addition, the data sets are frequently not even a sub-sample of the trees sampled for to establish the taper and volume functions.

Three different avenues could be followed to achieve a consistent estimation of biomass: (1) The use of expansion factors, (2) the application of stem biomass models, or (3) the combination of taper and density models.

A straightforward method to integrate biomass in growth simulators is based on expansion factors. Biomass expansion factors (BEF) serve as multipliers to convert timber volume to biomass and are widely applied in tropical and subtropical regions (e. g. Brown et al. 1989; Chhabra et al. 2002; Dovey 2009). Since the stem is the main contributor to tree biomass this approach usually produces plausible results. However, expansion factors linked to the stem volume only are constrained to the use within the same silvicultural treatment of the parameterisation data. They are not particularly suited to adapt to changes in the relationship between stem volume and aboveground tree biomass. Examples of such a situation are trees in the understorey, that have overproportionally more stem biomass as a result of suppressed crowns or also trees growing with single-sided competition that might branch earlier and have substantially more branch biomass (Ackerman et al. 2013a). This is the reason why the use of constant BEFs without further adaptations has been criticised (Soares and Tome 2004).

A second, widely used modelling approach is based on stem biomass-models, which are constructed according the established technique of taper functions. An appropriate modelling method was introduced by Parresol and Thomas (1991) and further refined by Jordan et al. (2006). A definite advantage of such an approach is that it is easy to keep it consistent with existing taper functions and volume models. Another advantage is that stem biomass can be predicted for any cut-off diameter. But one disadvantage is that the wood density is fixed in the model and cannot be adapted easily to new growing conditions of the tree which might limit the generality of the model. It must also be noted that the crown biomass is not covered by the model and has to be modelled additionally, e. g. with allometric models.

A third alternative is the modelling approach based on linked taper and density models (Seifert et al. 2006). Stem biomass is simulated spatially based on taper — equations for volume determination and a separate wood density model, which predicts basic wood density as a function of tree ring growth. While the disadvantage is that the taper and density models might originate from different data sets this model can adapt to different silvicultural treatments and extreme growth conditions can be simulated reliably as well. However, this approach does also not cover crown biomass. A possible solution, also applicable to stem biomass models as well, is to develop a model for the estimation of biomass proportions, e. g. the ILR-transformed model described earlier, and simulate foliage and branch biomass according to the obtained proportions simply by multiplying the obtained stem biomass with the proportion. All other biomass fractions can then be determined because an absolute value for the stem biomass is fixed and the proportions are known. This way it is possible to establish a fully consistent modelling system for the simulation of volume, biomass and biomass composition with all the advantages of flexibility with respect to silvicultural treatment (including wood density changes) and flexible cut­off diameters in the tree harvesting process.

3.4 Conclusions

An important observation in biomass modelling is the manifold of different approaches. Despite numerous efforts no real or de facto standards for sampling and modelling have been established so far, which complicates a comparison of studies and might confuse people wanting to inform themselves about biomass modelling. This point is particularly valid for error budgeting. Different methods and descriptors of error are prevalent. It is no wonder that Cunia (1990) warned from accepting existing methods of error budgeting without prior reflexion. However, a diversity of methods also gives evidence for a dynamic field of science that is still in its evolution. Many aspects, such as the error budgeting and the seamless integration of models in growth and yield simulators still have scope for future improvement.

This chapter is intended to act as a structured guideline for interested researchers and practitioners through the quagmire of biomass modelling and will hopefully be a valuable support despite its many places where explanatory text could not be extended by examples but had rather to be based on references.