An exercise for carbon sequestration by trees
By Larry McPheron
Adjunct Professor of Environmental Science at Kishwaukee College
Editor’s note: After reading our editorial “Restoration means clear cutting?” , Professor McPheron offered to show how much carbon is lost by cutting down one tree. The following exercise has been given to various high school and college students to show a method of calculating carbon sequestration provided by trees. We like to challenge our readers. See how your algebra skills do with these calculations, and send them to the Winnebago County Forest Preserve District.
Trees represent, in the minds of many, one of the solutions to global warming. Reforestation campaigns in Australia, Africa, North America, and elsewhere have been undertaken in an effort to capture and store, i.e., sequester, some of the excess carbon dioxide which is accumulating in the atmosphere. In fact, many who burn wood for home heating have assuaged their guilt by planting a new tree for each one that they have cut down.
This exercise will help you to understand the effectiveness of such action. It may also shed some light on the idea of purchasing carbon credits.
Two scenarios are examined below. In scenario I, the mature tree is harvested with the wood being used as fuel. In scenario II, the trees are scheduled to be harvested using the wood as building material.
An oak tree 75 feet tall, 3 feet d.b.h.(diameter breast height), and 150 years old is cut and used as fuel. We will consider only the trunk of the tree, which we will assume to be cone-shaped. It will be replaced by an 8-year-old seedling that is one-quarter of an inch (.0208 ft.) in diameter and 8 1/2 inches (.7083 ft.) tall. The shape of this seedling will also be assumed as a slender cone shape.
Given: Volume= 1/3 ~ R h
Surface area= ~R s
Length= s= R + h
Remember that the wood of a tree is derived primarily from carbon dioxide during photosynthesis and growth, and that the carbon dioxide is released into the atmosphere when the tree is burned.
First determine the relationship which exists between the volume of the mature tree and that of the seedling.
Mature tree: v= 1/3 ~ R h
v= 1/3(3.1415) (1.5 ) (75 0
v= (1.0471976) (2.25) (75)
v= 176.7146 cubic feet
Seedling volume: v= 1/3 ~ R h
v= 1/3(3.1415) (.0104 ) (.7083)
v= (1.0471976) (.0001082) (.7083)
v= .0000803 cubic feet
If one wished to replace the mature tree with an equal volume of wood, how many young seedlings would he need to plant to replace the mature tree?
Vol. of mature tree — 176.7146 cu. ft.
Vol. of seedling — .0000803 cu. ft.; 2,200,679.95 seedlings
Assume that the mature tree is still living and growing, adding 1/32 of an inch growth ring each year. Thus, cutting and removing the tree from the community will eliminate its carbon dioxide sequestering ability. If we assume that the seedling will grow at the same rate as the mature tree , how many seedlings will need to be planted to sequester the carbon dioxide that would have been sequestered by the mature tree? In this example, one must envision a layer of wood 1/32 of an inch thick to be laid down on the surface of the cone-shaped trunk of each tree and then compare one to the other.
First, the value of s must be determined for each tree.
Mature tree: s= R + h — seedling tree= s= R + h
s= 1.5 + 75 — s= .0104 + .7083
s= 2.25 + 5625 — s= .0000108 + .5017
s= 75.01499 ft. — s= .7083076 ft.
Having determined the value of s, the surface area of each tree can be determined as follows:
Mature tree Seedling tree
s= ~ Rs s=~Rs
s= (3.1415927)(1.5)(75.01499) s= (3.1415927)
s= 353.49981 sq. ft. s= .0231422 sq.ft.
The relationship of the two trees would then be seen by dividing the surface area of the mature tree by the surface area of the seedling tree or:
353.49981 sq. ft. / .o231422 sq. ft. = 15, 275.1
Consider the extension of that. If the mature tree is burned, during their first growing season, it will require 2,932,199.1 seedlings to sequester the equivalent amount of CO2.
One last consideration for you to contemplate is that some 34 percent or so of a tree’s carbon sequestration is done by its roots. Also, since all of the above-ground calculations are nearly applicable to the shape of conifers because they have a closer to conical shape and have smaller side branches, there needs to be an adjustment for the shape and branching pattern of deciduous trees. What should that adjustment be on average? I think it should be about 50 percent. What do you think?
And oh, by the way, how many people do you know planting 2,932,199.1 seedlings a year? Every standing, mature tree counts.
From the April 9-15, 2014 issue