1. Carbon Sequestration in Campus Trees
SSAC2006.QC879.8.RC1.1
Carbon Sequestration in Campus Trees
Can trees help offset carbon dioxide buildup from human activities?
Core quantitative skill
Power function
This module calculates the amount of carbon that is stored in trees on campus over a time interval of a year.
Quantitative concepts and skills
Order of Magnitude & Scientific Notation
Allometric relationships
Interpretation of exponential and logarithmic expressions
Percentage increase
Prepared for SSAC by
*Robert Cole – The Evergreen State College*
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. *2006*

2. Overview of Module Slide 3 – Presents the problem
Slide 4-7 – Give background on the mathematical approach to the problem, power functions and allometry.
Slides 8, 9 – Present the data set for a stand of ten trees in the Pacific Northwest.
Slide – Build the spreadsheet that calculates the sequestered carbon in the ten trees.
Slides 14 – Repeats the calculation using data from the preceding year and compares the results for the two years to determine the change over the course of a year.
Slide 16 – Asks the End of Module Questions.

3. Problem
Human activities are currently releasing massive amounts of carbon dioxide, which is contributing significantly to global warming (end note 1). Trees, in photosynthesis, convert carbon dioxide into carbon biomass, and release oxygen as a byproduct. As trees respire, they convert some of their carbon biomass back into carbon dioxide. However, the net growth of a tree’s biomass represents a net storage (sequestration) of carbon in the tree. Growing more trees could help remove carbon dioxide from the atmosphere to offset the excess that humans are releasing. Many Native Americans describe trees as lungs of the earth.
This module is the first of several that can be used to calculate a net carbon budget for your college campus.
What is the amount of carbon that is stored in a set of campus trees over the course of a year?

4. Mathematical Methods in Biomass Determination
One method used to determine the carbon content of trees is to cut the tree, and its root stock, dry it all, and determine its mass. Such destructive methods are slow, site-specific, and labor intensive. Scientists have developed allometric approaches to biomass sampling. These methods predict difficult-to-measure aspects (like biomass) from attributes that are easily measured. Allometry is the study of relationships between growth and size of one portion of an organism and the growth and size of the whole organism. Allometric relationships are found by plotting data points of the size of one portion of the organism against the size of the whole organism. In this module, a tree’s total biomass will be predicted from measuring its diameter at breast height (dbh) and using a mathematical expression that connects the two. The expression was determined by fitting the data from a large number of destructive measurements. Each tree species has its own mathematical expression connecting dbh and biomass.

5. The Form of the Allometric Equations For the Power Function
It is not uncommon in biology to find allometric relationships that can be expressed as power functions (end note 2):
y = c * x b (1)
A characteristic of power functions is that they become straight lines when plotted on log-log graphs (when both axes are logarithmic scales). Specifically, we can see that by taking the natural logarithm of each side of Equation 1, we obtain:
ln y = ln c + b * ln x (2)
The form of Equation 2 shows that ln y is a linear function of ln x, which is why the power function plots as a straight line on a log-log graph (end note 3). The line has a slope of b.
Biologists often make scatter plots of the logarithms of measured data points and attempt to fit a straight line to the plot. The parameters determined by fitting a straight line are the vertical intercept and the slope, that is, ln c and b of Equation 2.

6. The Measured Parameters of the Allometric Equations
Although the logarithmic form of the allometric equation (Equation 2) may look less familiar than the standard form of the power function (Equation 1), it is the logarithmic form that is reported in the research literature by forest ecologists who have attempted to determine relationships between a tree’s biomass and more readily measured features of the tree.
Forest ecologists who have determined allometric relationships for determining a tree’s total biomass have made many log-log correlations between the total biomass and the more readily measured variables. A commonly used variable is the diameter at breast height, usually labeled as dbh. Virtually all forest ecology textbooks use the notation dbh for this variable, although a single letter could be easily substituted. Similarly, the stem biomass of the tree is usually denoted as bst (standing for “biomass stem”). An excellent source of allometric relationships can be found in a public-domain database, Biopak, available from the US Forest Service at
(accessed August 14, 2007).

7. The Form of the Allometric Equations for the Given Set of Trees
The set of trees listed in the next slide is from one site in the Pacific Northwest. The trees are all of a diameter of less than 100 cm. The form of the equation that connects stem biomass to dbh for trees in this size range and for the species involved is:
ln (bst) = a + b * ln (dbh)
where bst is stem biomass. The parameters a and b are species-specific. They are also units-specific. The convention is that dbh is in centimeters and bst is in grams.
Had the trees been of a diameter larger than about 150 cm a different allometric equation would have been necessary. Different stages of a tree’s life have different equations relating biomass to dbh.
You can start to take data on a set of trees on your own campus if you identify the set of trees, determine the species of each, and measure the diameter at breast height of each at annual intervals. The allometric equations and species-specific parameters can be found in Biopak, mentioned in the previous slide.

8. The parameters a and b in the expression
The Given Set of Trees
The given set of trees consists of three silver firs, five Douglas firs, and two western hemlock.
The parameters a and b in the expression
ln (bst) = a + b * ln (dbh)
are as follows:
a b
Silver Fir (end note 4)
Douglas Fir
Western Hemlock

9. Constructing your Spreadsheet
Create an Excel spreadsheet that has the following information in it. These are measured data on a set of trees in the Pacific Northwest.

10. Computations with Your Spreadsheet
Now, in Column D, create a formula that relates the natural logarithm of stem biomass (bst) to the measured dbh. In Column E create a formula that computes bst from the expression ln (bst).
In Column F, we calculate the mass of carbon, which, for virtually all species of trees, is one-half of the value of bst.
Note. Scientific notation
Before proceeding, check your cell equations if your numbers don’t agree with the ones in the orange cells.

11. Completing the calculation for above-ground biomass
Having checked your calculations for Row 4, copy the formulas in Cells D4, E4, and F4 into Rows Use SUM in Cell F15 to calculate the total above-ground biomass for the ten trees.

12. Adding in the biomass of the roots
The calculation of the previous slide gives the total above-ground carbon in the stand of trees. Now we need to account for the carbon in the roots of a tree. Extensive (destructive) measurements have shown this to be % of the above-ground biomass for most species of trees. We will use the 20% amount (although you can change this amount for your species of trees if you have other data). This lower figure insures that our calculation will at worst underestimate the amount of sequestered carbon.
Add Column G, and populate it with a formula to increase the numbers in Column F by 20%.
Here’s our answer: the carbon in the ten trees in 2006.

13. Comparison with carbon stored a year earlier
After calculating the carbon sequestered in the trees in 2006, we immediately wonder how that differs from the stored carbon in the previous year. In order to easily make the comparison, it is helpful to condense the multi-stepped spreadsheet of the previous slides.
Review the cell equations in Columns D, E, F, and G in the spreadsheet of Slide 11, and combine them into a single equation for Column D in this spreadsheet. Build your equation one step at a time, comparing your results with those in the earlier spreadsheet. Watch your parentheses. This is not difficult. You just have to be careful.
Now we can make a comparison 

14. Tree data from a year earlier
Here are the data for Enter these new data into Column E. Copy the cell equations of Column D into Column F. What is the year-to-year increase in stored carbon in these ten trees? How does that change in biomass compare to the biomass in a single tree of this stand?

15. Caveat and Final Remarks
What we have NOT computed, but will be done in a subsequent module, is the carbon production from the decay of leaf fall (litter), and the carbon production from down woody debris (fallen branches, fallen trunks, etc.). This decay adds carbon dioxide to the atmosphere (why?), and so this carbon flux will have to be subtracted from the carbon sequestration you have just calculated.
However, the decay component represents a usually small correction to the number you have just obtained. For now, you have completed the computation of carbon sequestration for the set of ten trees.
Trees take up carbon dioxide from the atmosphere and store it in the mass of the tree. Planting more trees could help offset CO2 produced from the burning of fossil fuels up to a point. The amount of carbon sequestered in the young tress in this example is roughly 105 grams, or 100 kilograms. This corresponds to 367 kg of CO2 taken from the atmosphere (atomic weight of C is 12; molecular weight of CO2 is 44; and 100kg * 44/12 is 367 kg to three significant figures).

16. Caveat and Final Remarks, 2
Now, 367 kg of CO2 is approximately the amount of carbon dioxide produced by driving a car that gets 20 miles to the gallon of gasoline a distance of 833 miles. Thus it would take a larger stand of trees than these ten young ones to offset the driving habits of most Americans.
As these trees grow in diameter, however, they will take up carbon at an increasing rate (over the range of diameters listed for the allometric equations). As a result, we can expect that the trees will become increasingly useful as carbon offsets.
Ultimately, toward the end of a tree’s life, its rate of carbon uptake declines. Then when the tree dies, it releases CO2 to the atmosphere over the time of its decay. A fascinating article about whether it makes sense to cut old-growth trees (which take up carbon dioxide at a slow rate) in order to replace them with younger trees that take up CO2 at a faster rate is: “Effects on Carbon Storage of Conversion of Old-Growth Forests to Young Forests,” by Mark E. Harmon, William K. Ferrell, and Jerry F. Franklin, in Science, Vol. 247, No. 4943, (Feb. 9, 1990), pp

17. Caveat and Final Remarks, 3
The paper drew this conclusion: the carbon stored in old trees is so large that it would not be replaced by a stand of younger trees for at least 200 years. The authors demonstrated that the conversion of old-growth forests to tree plantations in the last 100 years has resulted in a net increase of carbon dioxide in the atmosphere.
Our conclusion here is that it makes more sense to be planting trees (lots of them), rather than to be logging them, and that growing trees will offset some, but not all, of the CO2 produced by burning fossil fuels for human activities.

18. End of Module Questions
1. Draw a diagram of the process you’ve just gone through with this spreadsheet. Start with the measurements of diameter at breast height (dbh) that you used as input data. Label the various parts of the process and include the units of the quantities computed.
Explain in one or two sentences how the carbon content of a tree is related to its diameter at breast height.
Make a graph that compares the amount of carbon stored by the three different species each of trees. Plot carbon stored vertically, and dbh, from 10 cm to 50 cm, horizontally.
If you had been given data measured on the same set of trees from ten years ago, rather than one year ago, explain how you would expect the annual rate of carbon sequestration to differ from what you computed.
Write the standard power-function form of the allometric equation for Douglas fir and western hemlock from the information in Slide 8 and end note 4.
Explain the value of the allometric equation in a problem such as the one discussed in this module.

19. End Notes
For more about the human contribution to global warming see: Intergovernmental Panel on Climate Change, Working Group I: The Physical Basis for Climate Change (accessed August 14, 2007). For further information from the Intergovernmental Panel, go to (accessed August 14, 2007). Return to Slide 3.
Be careful not to confuse the power function y = axb, with the exponential function y = abx. In the power function, the exponent is a constant (b). In the exponential function, the exponent (x) is a variable. Return to Slide 5.
In contrast, the exponential function plots as a straight line when the logarithm of y is plotted against x. Return to Slide 5.

20. End Notes (continued)
4. So, in logarithmic form, the allometric equation for silver fir is
ln (bst [grams]) = ln (dbh [cm]).
In standard form of the power function, it is
bst[grams] = dbh[cm]2.5867,
Where bst is in grams, and dbh is in cm. Return to Slide 8 .