Sophisticated data analysis will help you spot patterns, trends and relationships in your results. Data analysis can be qualitative and/or quantitative, and may include statistical tests.

## Calculating the carbon content of a tree

This assumes that you have measured

• the circumference of the tree at chest height
• the height of the tree

Note that for this method to work, the tree trunk radius must be greater than 25cm (or circumference must be greater than 157cm)

There are four steps to calculating the carbon content of a tree

• Step 1. Calculate the volume of the tree trunk
• Step 2. Calculate the biomass of the tree trunk
• Step 3. Estimate the biomass of the canopy and the root ball
• Step 4. Calculate carbon content based on the biomass of the whole tree

These steps are based on the analysis used in the carbon assessment protocol produced by Forest Research (link to pdf), the research agency of the Forestry Commission.

### Step 1. Calculate the volume of the tree trunk

#### (a) Calculate the radius of the tree trunk at chest height

$$\mathsf{Radius = \frac{circumference}{2\;\times\; \pi}}$$

e.g. if you measured the tree circumference to be 3m

$$\mathsf{Radius = \frac{3}{2\;\times\;3.14}}$$ $$\mathsf{Radius=0.48m}$$

#### (b) Calculate the volume of the tree trunk above ground

The approximate volume can be calculated by assuming that the tree trunk is a cone. Use the standard formula for calculating the volume of a cone.

$$\mathsf{Volume\;of\;the\;tree\;trunk = \pi \;r^2 \; \times \frac{height}{3}}$$

e.g. if the radius of the tree trunk is 0.48m and the height is 15m

$$\mathsf{Volume\;of\;the\;tree\;trunk = 3.14 \;(0.48)^2 \; \times \frac{15}{3}}$$ $$\mathsf{Volume\;of\;the\;tree\;trunk = 3.62\;m^3}$$

### Step 2: Calculate the biomass of the tree trunk

The biomass of the tree trunk can be calculated by

$$\mathsf{Biomass = volume \;\times\; nominal\;specific\;gravity}$$

If you know what species of tree that you have measured (like oak, ash or larch), you can find precise figures for nominal specific gravity figures on page 46 of the carbon assessment protocol (link above). Alternatively use the figures below

For broadleaved trees, nominal specific gravity = 0.53
For conifers, nominal specific gravity = 0.39
e.g. if the volume of the tree trunk is $$3.62\; m^3$$and the tree is an ash tree (a broadleaved tree)

$$\mathsf{Biomass = 3.62 \;\times\; 0.53}$$ $$\mathsf{Biomass = 1.92 \;oven\;dry\;tonnes}$$

### Step 3. Estimate the biomass of the canopy and the root ball

As well as the tree tunk, a substantial amount of carbon is stored in the tree’s canopy (or crown) as well as below ground in the roots.

The biomass of the crown and the roots can be estimated if the radius of the trunk and the species of tree are known. This method is based on the analysis used by Forest Research.

#### (a) Estimate the crown biomass

First take the radius and double it to get the tree’s diameter at breat height (DBH). Make sure that this is expressed in centimetres.

There are two ways to calculate the crown biomass, depending on whether the tree is large or small. A large tree has a diameter at breast height of more than 50cm. A small tree has a diameter at breast height of between 7cm and 50cm. Smaller trees cannot be assessed using this method.

If DBH is 7-50cm then $$\mathsf{Crown\;biomass = a \times DBH^b}$$

If DBH > 50cm then $$\mathsf{Crown\;biomass = c + (d\;\times\;DBH)}$$

$$a$$, $$b$$, $$c$$ and $$d$$ are species-specific constants shown in the table below.

Estimating crown biomass
Species a b c d
Larch 0.000044 2.0291 -0.129047 0.005039
Corsican pine 0.000012 2.4767 -0.299529 0.009949
Lodgepole pine 0.000018 2.4767 -0.430537 0.014300
Scots pine 0.000016 2.4767 -0.394206 0.013094
Douglas fir 0.000017 2.4767 -0.411768 0.013677
Grand Fir 0.000015 2.4767 -0.353198 0.011732
Noble Fir & other conifers 0.000015 2.4767 -0.353198 0.011732
Hemlock 0.000015 2.4767 -0.353198 0.011732
Norwegian Spruce 0.000015 2.4767 -0.353198 0.011732
Cedar 0.000015 2.4767 -0.353198 0.011732
Sitka Spruce 0.000015 2.4767 -0.353198 0.011732
Beech, Sycamore & Maple 0.000019 2.4767 -0.459519 0.015263
Oak and all other broadleaved trees 0.000017 2.4767 -0.411551 0.013670

e.g. if the DBH is 96cm and the tree is an ash tree (in “all other broadleaved trees”)
$$\mathsf{Crown\;biomass = -0.411551 + (0.013670 \times 96)}$$
$$\mathsf{Crown\;biomass = 0.932\;oven\;dry\;tonnes}$$

#### (b) Estimate the root biomass

Next you can estimate the biomass of the roots. Again the equation that you use depends on the size of the tree. Remember that the DBH must be expressed in centimetres.

If DBH is 7-50cm then…

$$\mathsf{Root\;biomass = e \times (DBH)^{2.5}}$$

If DBH > 50cm then…

$$\mathsf{Root\;biomass = f + (g \times DBH)}$$

$$e$$, $$f$$ and $$g$$ are species-specific constants shown in the table below.

Species e f g
Larch 0.000017 -0.133480 0.007296
Corsican pine 0.000011 -0.082603 0.004515
Lodgepole pine 0.000017 -0.133480 0.007296
Scots pine 0.000015 -0.118673 0.006487
Douglas fir 0.000017 -0.133480 0.007296
Grand Fir 0.000015 -0.118673 0.006487
Noble Fir 0.000011 -0.082603 0.004515
Hemlock 0.000015 -0.118673 0.006487
Norwegian Spruce & other conifers 0.000012 -0.091547 0.005004
Cedar 0.000011 -0.082603 0.004515
Sitka Spruce 0.000021 -0.157579 0.008614
Beech 0.000023 -0.174882 0.009559
Oak and all other broadleaved trees 0.000023 -0.174882 0.009559

e.g. if the radius is 96cm and the tree is an ash tree (in “all other broadleaved trees”)
$$\mathsf{Root\;biomass = -0.174882 + (0.00959 \times 96)}$$
$$\mathsf{Crown\;biomass = 0.785\;oven\;dry\;tonnes}$$

## Step 4. Calculate carbon content based on the biomass of the whole tree

#### (a) Find the biomass of the whole tree

$$\mathsf{Biomass\;of\;whole\;tree = Trunk\;biomass + Crown\;biomass + Root\;biomass}$$

e.g. if the trunk biomass is 1.92 oven dry tonnes, the crown biomass is 0.932 oven dry tonnes, and the root biomass is 0.785 oven dry tonnes
$$\mathsf{Biomass\;of\;whole\;tree = 1.92 + 0.932 + 0.785}$$
$$\mathsf{Biomass\;of\;whole\;tree = 2.64\;oven\;dry\;tonnes}$$

#### (b) Find the carbon content of the tree

The carbon content of the tree is calculated as

$$\mathsf{Carbon\;content = \frac{Biomass\;of\;whole\;tree}{2}}$$

e.g. if the biomass of the whole tree is 2.64 oven dry tonnes

$$\mathsf{Carbon\;content = \frac{2.64}{2}}$$ $$\mathsf{Carbon\;content = 1.32\;oven\;dry\;tonnes}$$

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