View source for Biomass functions and carbon estimation

==Constructing biomass functions==

[[File:2.8.5-fig42.png|right|thumb|400px|'''Figure 1''' Relationship  between dbh, tree height and aboveground biomass on a metric (original)  scale (left) and after logarithmic transformation of the variables  (right) (Kleinn 2007<ref name="kleinn2007">Kleinn, C. 2007.  Lecture Notes for the Teaching Module Forest Inventory. Department of  Forest Inventory and Remote Sensing. Faculty of Forest Science and  Forest Ecology, Georg-August-Universität Göttingen. 164  S.</ref>).]]

For the construction of biomass functions, a data set with observed biomass and [[Diameter at breast height|DBH]] or DBH and [[tree height]] is required, for example. However, individual tree biomass is a variable that cannot be measured directly so that also the observation of individual tree biomass is usually sample based. Therefore any estimation of biomass is not affected by a measurement error alone, but carries further errors as result of modeling.
Destructive sampling of the different biomass compartments of an individual tree is the standard approach, where normally the main compartments leaf/needles, branches, stem and roots are treated separately for practical reasons as well as for differences in the wood density between these different functional parts.
While the whole compartment is weighted for its fresh mass in the field, only samples from each compartment are taken to lab for oven drying (at about ~105°C until weight is stable). The relation between fresh and dry mass is then used as ''conversion factor'' for the whole compartment. 

The dry weights of compartments can be correlated separately or summed up to the overall aboveground biomass. In cases that also the root system was sampled, the belowground part can be incorporated to calculate the total biomass. In the context of carbon budgeting on large scale or national level, the approved methodologies of the IPCC (Intergovernmental Panel on Climate Change) for the calculation of greenhouse gas balances further propose so called [[Biomass Expansion Factors]] (BEFs) for biomass quantification. BEFs are derived as relationship between [[stem volume]] and (aboveground) biomass as:

:<math>BEF_i=\frac{W_i}{V_{stem}}\,</math>,

where:

:{|
|-
|<math>W_i\,</math>
|=
|dry weight (Kg)
|-
|<math>V\,</math>
|=
|Volume (m³)
|-
|<math>i\,</math>
|=
|total tree or compartment.
|}

BEFs are simple “biomass functions”. Because the relative shares of different [[tree compartments]] are changing over the tree age, BEFs are not stable over a trees lifetime. New approaches therefore try to derive age-depending BEFs. Even if criticised concerning their uncertainty and inflexibility BEFs represents the only feasible pathway to carbon assessment for many developing countries, where forest inventories and reliable, recent data on growing stock volumes and increment are rudimentary or missing.


{| 
|'''Table 1:''' Series of three conversion factors whose combination allows converting<br>stem volume to total biomass C-content (from Karjalainen and Kellomäki 1996<ref name="karjalainen_kellomäki1996">
Karjalainen T and S Kellomäki. 1996. Greenhouse gas inventory for land use changes and forestry in Finland based on international guidelines. Mitigation Adapt. Strategies Global Clim. 1:51-71</ref>).
{| class="wikitable"
! colspan="2" |<math>cf=ef*x*dw*x*cc</math>
|-
|<math>cf\,</math>
|Conversion factor from stem volume to total biomass C-content
|- 
|<math>ef\,</math> 
|Expansion factor from stem volume to total tree biomass
|-
|<math>dw\,</math>
|Conversion factor to dry matter
|-
|<math>cc\,</math>
|C-content
|}
|}

 
The expansion factor approach can also be applied for tree carbon estimation, because wood carbon content is fairly constant. By combining three conversion factors, one arrives then a conversion factor that converts stem volume (which is a standard result of [[Forest inventory|forest inventories]]) into total biomass carbon content.