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The method behind constructing the “Calculate the CO2 Sequestered in your Tree”
with a postscript The Method as a Learning Activity
 

The CO2 a tree stores is dependent on its weight but in attempting to make a species flexible CO2 sequestering calculator, tree volume calculations are used as  the basis. Volume is mostly a dependent on a trees shape but is independent of wood density one of the major differences between species. Volume can be be multiplied by the density of the trees timber to calculate its weight, then the carbon and CO2 amounts.
 

When selecting equations and assumptions to base the calculation on only results based on the physical sampling of real trees were used. Calculating the above ground timber volumes of standing trees is a common forestry practice and in researching and testing appropriate equations the volume of bark and leaves are also studied. Below ground there seems to be more guess work than research work although with the raising interest in CO2 offsetting one study has now being published.
 

The equations for calculating tree above ground volume are from the Georgia Forestry Commissions Research Paper 60 “Total-Tree Weight, Stem Weight, and Volume Tables for Hardwood Species in the Southeast,” Alexander Clark III, Joseph R. Saucier, and W. Henry McNab, Research Division, Georgia Forestry Commission, January 1986.
 

In over thirty locations in South Eastern USA eight species of trees were extensively surveyed. Using the tree’s trunk diameter and it’s height, equations for their volume and weight were developed. Then the trees were cut and weighed and the equations analyzed.
 

This calculator is based on their final equations:
 

Calculating Above Ground Total Wood Volume
 

DIA>11inch  Volume wood = a(DIA²)^b(HEIGHT)^c
 

DIA<11inch Volume wood =e(DIA²xHEIGHT)^f
 

Where a, b, c, e & f are co-efficient developed for each species.
The volume of a tree is influenced by its shape but independent of its wood density so when applying these equations to other species commonality of shape has the greatest influence on their accuracy.
 

NOTE: During this research when looking at CO2 sequestration calculations one misunderstanding when using %'s was common. For instance it was common to assume the weight of say the roots are 20% of the total weight of a tree, then 120% x Above Ground Weight was used as the Total Tree Weight. Yet assuming that something is 20% of a total also assumes that the rest is only 80% of that total. So the correct Total Tree Weight is the Above Ground Weight divided by 80 (gets 1% of total) then multiplied by 100 or 125% X Above Ground Weight. It can seem confusing but can lead to significant errors to the end result. (if A is Y% of a Total then the Total = The Rest x 100/100-Y)
 

Adding Bark to Total Wood Volume
Although the volume of bark was not included in the calculation this and other studies [2] [3]  have weighed bark and expressed it as %’s of total green tree weights. Assuming density is similar these can be used to calculate total tree (wood, bark and foliage) green volumes. On average Bark is 25% of total tree weight (wood + bark) or 33% of wood only weight. ) (see Addendum 1)
 

Adding Foliage to Total Wood & Bark Volume
Foliage was also not included in the calculation In the case of deciduous trees it is not a factor in annual CO2 sequestration although in evergreen trees it is included. Again this and other studies [2] [3]  have weighed foliage and expressed it as %’s of total green tree weights. Foliage % weights were also analyzed in regard to position, whether upper or under story or growing in the open. These can be used to calculate total tree (wood, bark and foliage) green volumes.  On average foliage is 30% of wood & bark weight. For needles it is 22%. Trees in the under story have ~30% less foliage than the upper story while trees in the open ~ 20% more.  (see Addendum 2)
 

Adding Below Ground roots to Total Tree Volume
The weight and volume of tree roots are even less studied and have been mostly guessed at. Research is limited and results highly variable. The Australian Greenhouse Office figures are used. They are roots are 20% of above ground for Softwood and 25% for Hardwoods. The IPCC recommends 20% for all types. It is generally acknowledged theses are underestimations as the sampling techniques ignore the roots directly below the main trunk and the roots extend below sampling depth.. It is also acknowledged that the roots increase as trees are under greater environmental stress so it increases significantly in arid areas where roots may be greater than above ground.  (see Addendum 3)
 

Converting Total Tree Volume to Total Tree Weight
Once Total Tree Volume is determined to calculate the Total Tree Weight is just a mater of multiplying by the density. Dried Timber Densities [7] [8]  are available for a wide range of tree species so calculating the trees total dry weight is possible.
Determine the weight of carbon in the tree
The average carbon content of dried timber, bark & leaves is generally 50% [6]  Therefore, to determine the weight of carbon in the tree, multiply the dry weight of the tree by 50%.
 

Determine the weight of carbon dioxide sequestered in the tree
CO2  is composed of one molecule of Carbon and 2 molecules of Oxygen.
The atomic weight of Carbon is 12.001115.
The atomic weight of Oxygen is 15.9994.
The weight of CO2  is C+2*O=43.999915.
The ratio of CO2  to C is 43.999915/12.001115=3.6663.
Therefore, to determine the weight of carbon dioxide sequestered in the tree, multiply the weight of carbon in the tree by 3.6663[6]
 This is the final result.

 

Addendum 1 Abstract G.F.C. Research Paper 39 1982
 

Total Tree and Firewood Weights and Volumes of Scrub Oaks in the Georgia Sandhills
H McNab Georgia Forestry Commissions Research Paper 22 1981
 Summary of Results (124 trees sampled)

At 467 trees per acre there was 35.8 tons Bio-Mass per acre 34 tons in trees greater than 3inch diameter (Mean tree dia 4inch)
Equations Derived: Total Tree Vol 0.06709([Dia Inch]2)1.18482 or 0.00714(Hx[Dia Inch]2)0.91840
Wood only Vol 0.02730([Dia Inch]2)1.35056

 

Addendum 2 Abstract G.F.C. Research Paper 39 1982
 

Total-tree Green Weights of Sapling-Sized Pines in Georgia
D Philips & H McNab Georgia Forestry Commissions Research Paper 39 1982
Summary of Results (500 Trees sampled. Species: Lodlolly, Longleaf, Shortleaf, Slash & Virginia Pines)

The study gives an indication of site on tree growth and shape with crowns being about 60% heavier in open grown over under-story growing sites trees. Foliage varied from 13 to 5lb for 3inch Dia trees, with open grown trees 5-10 years younger. Open grown trees were shorter but heavier. tions ( y=a(D2)b or y=a(D2H)b where y=total_green_weight, D2=diameter_breast_height_squared H=total_tree_height a, b=regression_coefficients ) were tested with coefficients formulated for the different geographical and growing locations. It was noted that the diameter only equation although less accurate was less effected by location differences.
 

Addendum 3 AGO National Carbon Accounting System Technical Report 5b. Review of Allometric Relationships for Estimating Woody Biomass for New South Wales, the Australian Capital Territory, Victoria, Tasmania and South Australia by Heather Keith Damian Barrett Rod Keenan
 Review of estimated ratios of below-to-aboveground biomass from the literature

References:
[1] http://www.forestdisturbance.net/publications/GF%20RP60-Clark.pdf
[2] “Total Tree and Firewood Weights and Volumes of Scrub Oaks in the Georgia Sandhills” H McNab Georgia Forestry Commissions Research Paper 22 1981
[3] “Total-tree Green Weights of Sapling-Sized Pines in Georgia” D Philips & H McNab Georgia Forestry Commissions Research Paper 39 1982
[4] “Carbon Dioxide Reduction and Carbon Sequestration by Co-Firing Tree Energy Crops in Florida’s Coal-fired Power Plants” S Segrest, The Common Purpose Institute
[5] ” Richard A. Birdsey, United States Department of Agriculture Forest Service, Northeastern Forest Experiment Station, Radnor, PA, August 1992. http://www.ilea.org/birdsey/fcarbon_index.html#toc
 

Postscript
 

Using  Calculating the CO2 Sequestered in a Tree as a School Learning Activity
 

Determining the amount of CO2 sequestered in a tree is an ideal teaching exercise combining applied mathematics, chemistry and ecology.  By using surrounding trees as the examples it can illustrate how academic work can give insights to the world around us.
 

This is the process:
1  Determine the tree's height and trunk circumference.
2. Determine the total volume of the tree.
3  Determine the density of the tree.
4. Determine the weight of the tree.
5. Determine the weight of carbon in the tree.
6. Determine the weight of carbon dioxide sequestered in the tree.
 

Taking measurements of a tree particularly its height can provide a practical example of geometry as well as time in the sun. There are several different methods that can be used from climbing, using shadows or by trigonometry.  So it can also illustrate decision making.
 

If a forest or scrub is used as the example then the plot area also needs to be calculated adding a further geometry problem to solve as well as introducing sampling and statistics.
 

The basis of the volume equations of Volume= a( Diameter2 x Height )b are also practical examples of geometry.
 

Converting a tree’s volume to weight can be a research exercise of determining the species then the timber density of that species or of taking a sample and with a beaker of water and scales having a Archimedes “eureka!” moment.
 

Working out the amount of CO2 from the carbon content provides a practical example of the use of the period table as could finding the carbon content of cellulose.
 

Here are two educational websites who had conceived it as a learning activity for their students [1 & 2]
[1]  The National Computational Science Leadership Program
http://www.ncsec.org/cadre2/team18_2/students/purpose.html
[2] The Shodor Education Foundation
http://www.shodor.org/succeedhi/succeedhi/weightree/teacher/activities.html