Calculating forest carbon stocks This is a practical class I run with


Calculating forest carbon stocks This is a practical class I run with
Calculating forest carbon stocks
This is a practical class I run with my final year ‘Climate Change and Carbon Cycling’ class to reinforce
that week’s lecture on global carbon stocks in the terrestrial biosphere. I’ve provided some
annotations in red to give you a worked example and hopefully guide you through the process. You
may wish to simplify some of the steps and/or modify to suit to your own needs.
This is only one example of how simple measurements can be related to the bigger carbon picture
but hopefully this will give some ideas that you can use in your teaching.
I would be interested in hearing back about how you have used the ideas and if it worked well in
Gareth Clay, August 2016
[email protected] Twitter: @garethdclay
Aims of the exercise
1) To become familiar with the concept of allometry
2) To calculate the carbon stocks of a tropical forest based on a real dataset of measured trees
Measuring carbon stocks
There are different ways in which we can estimate the amount of carbon stored in forests. We can
take a ‘top-down’ approach where we look at a landscape scale often through remote sensing tools
e.g. satellite data. We can also use ‘bottom-up’ or inventory methods where we might look at
individual plots or land uses. Here the individual trees or stands of trees are directly measured to
estimate their size and biomass. Often satellite data is compared to these field measurements in
order to calibrate their estimates.
In this practical we are going to look at some of the steps in calculating the carbon stocks for a
tropical rainforest using an inventory approach.
What is (tree) allometry?
Allometry is the study of the relationship between size and shape of an individual e.g. animals,
organs. Imagine a cube of 1cm length (L) sides, the surface area (SA) is 6cm 2. At L=2, SA = 24; L=3,
SA = 54 etc. We can say that SA ∝ L2. Equally we can do the same with volume and length (Volume
∝ L3)
In the context of land use carbon stocks, tree allometry
establishes quantitative relationships between easy to
measure parameters and difficult to measure
parameters e.g. between tree diameter (easy to
measure; Figure 1) and total biomass (harder to
Figure 1. Calliper measuring tree
diameter (Elsner, G. 2006.
Wikimedia Commons, CC BY-SA)
Allometric Coefficients
Above we used the symbol “∝” to mean “is proportional to”. The trouble is this relationship
between the two variables is not an equation we can solve – we need to know something known as
the allometric coefficient.
To obtain the allometric coefficient, we could express the first variable as a function of the second,
using the general power equation:
(Equation 1)
y = βx
In this equation, α (alpha) is the allometric coefficient relating the x-variable to the y-variable.
The coefficient β (beta) is a constant.
In the case of the cubes earlier on, SA = 6L2 (hint: try working this out yourself to confirm this!).
Figure 2 shows some hypothetical relationships between surface area and volume of some fictitious
animals. The equations describe the best-fit lines in the form of Equation 1. In the case of A, β =
0.9842 and α = 0.6680; likewise in B, β = 1.0354 and α = 1.4945
Figure 2. Hypothetical curves between Surface Area and Volume (after Goldman et al., 1990)
Calculate the carbon stock of the Kakamega rainforest, Kenya, using allometric relationships and
literature values
Calculate allometric relationships
1) Open the Excel file “Tropical forest.xls”
2) Open the Worksheet titled “Data for allometry”. Here you find data for diameter at breast
height (dbh) and above-ground biomass for nearly 170 trees from moist tropical forests around
the world (Brown, 1997)
3) Using this data plot above-ground biomass against dbh.
4) Fit a power law trendline and r2
a. What is the equation? And what is the r2 value?
y = 0.1178x2.5324
R² = 0.9682
Power (Series1)
5) You now have an allometric relationship between biomass and dbh for moist tropical rainforests
in the form of y = βxα . i.e. y=0.1178x2.5324
Calculate biomass for an unknown dataset. The worked answers are given in the associated
6) Switch to “Kakamega data” worksheet. This sheet lists tree girth data from 36 trees collected by
Dr Gareth Clay and colleagues during fieldwork in January 2013 in a tropical rainforest in
western Kenya – Kakamega. (For more information on the Kakamega forest see Glenday (2006))
7) Firstly, you need to convert tree girth (circumference) into dbh values. Assume that the tree
trunk is circular. Circumference =π* diameter Divide circumference by pi.
8) Calculate the biomass in kg for each of the trees based on the general relationship you found
above. [Hint: In Excel, the symbol ^raises a number to a power]
9) The data comes from 3 different regions in the forest: A, B and C. Calculate the average tree
biomass in each of the 3 regions.
Calculate the carbon stock of the Kakamega forest
10) Calculate amount of carbon in each of the trees. Assume that 50% of the biomass is carbon
11) If we assume there is an average of 50 trees per hectare (ha) in the forest, calculate the average
carbon density (kgC/ha) for each of the 3 regions
12) Convert this to tonnesC/ha
13) There is approximately 3,000ha in region A, 14,000ha in region B and 600 ha in region C.
Calculate the total carbon stock in tonnesC for each of these sections and also calculate the total
carbon stock of the above-ground biomass in the Kakamega forest.
Average Tree
Biomass (kg)
Average C content per tree
Carbon density
(tonnesC per ha)
Total Carbon
1. Which of the regions has the greatest amount of carbon?
2. What can we say about the data quality? [Think about sample size for each region and how
standard deviations are affected].
Small sample size for section A (only two data point) lead to high StDev
3. Comment on the assumptions used throughout the calculations
Assumed the general allometric relationship for moist tropical forests holds true for this
forest in Kenya.
Assume 50% C is approx OK, but does vary from 40-55%
Trees per ha is probably low and is based on an estimate from Nigeria
Assumed trees are circular
4. Figures in Glenday (2006) suggest Region A should be ~280±77 tonnes C/ha; Region B ~330±63
tonnes C/ha and Region C 250±78 tonnes C/ha.
a. Are your numbers within the reported ranges?
b. How do your values differ from these values?
c. If the numbers are substantially different, what do you think could be causing the
Within range on A, but out of range on B and C (below)
Assumptions used are likely leading to differences. In scientific writing it is best practice to
state your assumptions.
Useful information
Power law equation: y = βxα
Carbon concentration = 50%
Average trees per hectare = 50
Circumference = π*dbh
Area section A = 3,000ha
Area section B = 14,000 ha
Area section C = 600ha
Further reading
GlobAllomeTree is an international web platform to share data for assessing volume, biomass and
carbon stock of trees and forests ( Here you can sign-up and
download a range of allometric relationships for different tree species and regions. I’ve not had a
chance to explore this database yet but looks really valuable – let me know if you find it useful!
Brown, S. 1997. Estimating Biomass and Biomass Change of Tropical Forests: a Primer (FAO Forestry
Paper – 134) FAO, Rome. Available at:
Glenday, J., 2006. Carbon storage and emissions offset potential in an East African tropical
rainforest. Forest Ecology and Management, 235(1–3): 72-83.
Goldman, C. A., Snell, R.R., Thomason, J.J. and Brown, D.B. 1990. Principles of Allometry. Pages 4372, in Tested studies for laboratory teaching. Volume 11. (C. A. Goldman, Editor). Proceedings of the
Eleventh Workshop/Conference of the Association for Biology Laboratory Education (ABLE), 195
pages. Available at:

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