ESCI 325: Fundamentals of Ecology

Homework #2: Carbon Cycling


In this lab exercise, we will be quantifying the amount of carbon being sequestered by a second-growth forest and compare this to the carbon being released to the atmosphere by a vehicle powered by an internal combustion engine.


The potential for substantial climate change resulting from increasing atmospheric concentrations of radiatively-active trace gases has motivated efforts to identify natural and anthropogenic sources and sinks for these gases (Houghton and Woodwell 1989, Post et al. 1990). Among these radiatively-active trace gases, carbon dioxide has the greatest potential to affect global climate and hence, the global carbon budget has received special attention (IPCC 1990). Recent global-scale estimates (Sundquist 1993, Houghton et al. 1992, Houghton 2000) suggest that emissions of CO2 to the atmosphere from the combustion of fossils fuels and land use account for 5.7  and 1.9 Pg of carbon per year, respectively. The oceans are thought to be a sink for 2.1 +- 0.8 Pg C / yr while observed increases in atmospheric CO2 concentrations account for about 3.2 Pg C / yr. This observed increase and the known sources leaves a "missing sink" in the biosphere of about 2.3 Pg C / yr. The search for this missing sink is at the core of much of the current work on global carbon budgets.

The certainty in the measurements of the various global carbon pools and fluxes varies widely. There have been economic incentives to carefully track the global consumption of fossil fuels and hence, there is more confidence in the estimates of fossil fuel emissions than for the other sources and sinks. Solomon et al. (1993) point out that the oceans and the atmosphere are reasonably well mixed systems and the measurement and modeling of carbon pools and fluxes between the ocean and atmosphere is a tractable problem in physical chemistry and fluid dynamics. For this reason, the estimates of carbon flux between the ocean-atmosphere systems have remained between a fairly narrow, but perhaps not accurate, range of values over the past 20 years (Keeling 1973, Tans et al. 1990, Orr 1993). Solomon et al. (1993) go on to point out that the terrestrial system is fundamentally different than the ocean and the atmosphere in that it is not at all well mixed with respect to carbon. In the terrestrial system, heterogeneity in carbon pools and fluxes exist at all spatial and temporal scales and results from a complex interaction of natural and anthropogenic factors. This heterogeneity has resulted in a wide range of estimates of terrestrial carbon sources and sinks.

The relative certainty in the other carbon pools and fluxes points towards a terrestrial carbon sink. Several lines of evidence suggest that the missing carbon sink is most likely to be found in northern, mid-latitude forests (Tans et al. 1990, Kauppi et al. 1992, Taylor and Lloyd 1992). Dixon et al. (1994) calculated that, if these forests are to account for the missing carbon in the global budget, their net accumulation rate must be about 1.5 Mg C / yr, or about 2 to 3% of their present standing stock. They point out that, although this is within the range of values observed at selected sites, it is considerably higher than the most recent estimate for the continental USA (0.4 Mg C/ha/yr; Turner et al. 1994) and it is up to four times higher than the observed globally-averaged rate of accumulation for northern temperate forests (reviewed by Dixon et al. 1994).

Efforts to reduce the uncertainty in the global terrestrial carbon budget will require better information about the spatial and temporal heterogeneity of carbon storage and carbon flux in various regions throughout the world. Forest ecosystems are particularly important in any consideration of global carbon budgets because they contain about 60% of the global terrestrial carbon stocks (Waring and Schlesinger 1985).


PNW Forests

The forests of the PNW are among the most productive in the world and contain many tree species that attain great ages and substantial stature (Waring and Franklin 1979). Several tree species achieve ages of 500 to 1000 years in natural forests that may contain individual trees 100 to 200 or more centimeters in diameter at breast height with tree heights of 60 to 80 meters. These forests have the capacity to store very large quantities of carbon. An intensively studied, 450-year-old Douglas-fir (Pseudotsuga menziesii) stand on moderately productive (site class 3) land in the central Oregon Cascade Mountains, contained 611 Mg of carbon per hectare in above- and below-ground living and detrital pools and in the mineral soil (Grier and Logan 1977, Harmon et al. 1986). Sixty-year-old stands on comparable land contain between 259 and 274 Mg of carbon per hectare in these same pools (Harmon et al. 1990).

Harmon et al. (1990) have shown that harvesting these old-growth forests and replacing them with young plantations results in a large net release of carbon to the atmosphere, even when storage of carbon in forest products is considered. Although young plantations have a higher net annual rate of carbon uptake than old forests, the total amount of carbon stored in young plantations is minimal when compared to old-growth stands. Harvesting an old-growth stand results in a large increase in the amount of dead wood on the site in the form of tops, branches and roots. Even if the decay rate remained constant after harvest, the amount of carbon released to the atmosphere from this very large detrital pool is substantial during the first several decades after harvest. Similarly, much of the carbon that is removed from the site by timber harvesting is quickly released to the atmosphere during primary and secondary manufacturing processes and by incineration and decomposition of short-lived forest products. Many decades are required before the net carbon accumulation rate by regenerating trees in the plantation exceeds the net carbon emission rate to the atmosphere by the detrital pools and the forest products sector. It may take 200 years before the total amount of carbon stored by the stand approaches pre-harvest levels.


Although these stand-level dynamics are well documented, developing a regional carbon budget requires the integration of these results in both the time and space domains. Integration in the spatial domain requires information on the distribution of stand ages, species, site productivity and management techniques. Integration in the time domain requires spatially explicit information on changes in stand age in response to timber harvest, wildfire, succession and changes in management practices and forest product utilization standards. Assembling this information is a challenging interdisciplinary problem in ecology, silviculture, economics, history and social science.

Units: In the text above, I used several standard abbreviations for large quantities of carbon.  I used Mg and Pg.  Do you know what these abbreviations mean?  If not, did you look this up?  If not, why not?  Take responsibility for your education!  Don’t simply skip over information that you don’t understand!  Mg is the abbreviation for Megagram.  Note that a megagram (Mg) should not be confused with a milligram (mg).  OK, so how many grams are in a Mg?  Pg is the abbreviation for a Petagram (see note below).  OK so how many grams are in a Pg?  You can find this information in lots of places, including on the web by doing a search using Google or some other search engine.

Note added 11/28/07: It turns out that I’ve been mis-spelling Pg for years.  I always thought it was “Pedagram” but it is actually “Petagram  If you google “Pedagram” you will find about 200 hits and if you google “Petagram” you get about 12,000 hits.  So, it’s fair to say that there are others out there who have mis-spelled it as I have.  Oops.



Carbon content of Gasoline: Gasoline is a mixture of several hydrocarbons, mostly heptane (C7H16) and isooctane (C8H18). The Aoctane rating@ is an estimate of the relative amounts of these two compounds. There are some other additives, however, for our purposes, we will ignore these. We will also assume that my truck is 100% efficient in the combustion of this gasoline. This is probably not correct (it is probably more like 90 to 95% efficient; note that I am talking about efficiency of combustion, not efficiency of conversion from chemical to mechanical energy; energy conversion efficiency for most internal combustion engines is about 20-25%) but the various emission control devices (like the catalytic converter) probably insure that nearly all the fuel is oxidized.

To calculate the carbon emissions, we need to calculate the carbon content of gasoline. The densities of octane and heptane are 700 and 684 g/l, respectively. Based on molecular weights, the proportion of each of these compounds that is carbon is:


            C = 8*12 = 96

            H = 18*1 = 18


114 ====> 96/114 = .84


            C = 7*12 = 84

            H = 16*1 = 16


100 ====> 84/100 = .84

This gives the mass of C in a liter of octane and heptane as 589g and 575g, respectively. For 87 octane gasoline (87% octane and 11% heptane), I get a figure of 576 g C/l.

Carbon Emissions by autos: At present the national average for all vehicles in the U.S. is about 18 miles to the gallon and the national average is about 10,000 miles per year  So:

10,000 miles per year / 18 miles per gallon = 556 gallons per year

 556 gallons per year * 3.785 liters per gallon = 2,103 liters per year

 2,103 liters per year * 576 g C per liter = 1,211,420 g C per year = 1.21 Mg C per year

Carbon Offset: OK, now we need to determine how much forest land would be required to balance the carbon emissions by the average car?


Carbon accumulations by a Second-growth Forest:  Assume you start with a second-growth forest composed entirely of Douglas-firs with an average Diameter at Breast Height (DBH) of 50 cm.  Using DBH (in centimeters), the current biomass (in grams) of each tree can be calculated using the following equations:

Bark/Bole biomass=EXP(2.902625+(2.4818*LN(DBH)))+EXP(4.841987+(2.3323*LN(DBH)))  



NOTE: In the equations above, the “EXP()” is an Excel function that takes the base of the natural log and raises it to the power of the stuff inside the parenthesis.  So, this is equivalent to the “ex” button on your calculator.  Similarly, the “LN()” in the equations above is an Excel function that takes the natural log of the value inside the parenthesis.  I’d strongly recommend that you use Excel to do these calculations.  To make it even easier, simply copy-paste the equations above into Excel, then substitute the appropriate DBH value into the equation.

Add all this up to determine the total biomass of each tree.

Now assume that each tree adds 0.5 cm to its diameter each year.  Calculate the biomass of a tree with a DBH of 50.5 cm.  Now assume a tree density of 100 trees per hectare.  Calculate the rate of biomass accumulation (in Mg/ha/yr) for this forest.  Note that the rate of biomass accumulation (Mg/ha/yr), i.e, the change in biomass over time, is simply:

dBiomass/dt = [(Mg/ha at time t) – (Mg/ha at time t-1)] / 1 yr

It is important to recognize that these three equations give you DRY BIOMASS.  Much of this includes elements other than carbon.  Recall that I told you in class that ABOUT HALF OF THE DRY BIOMASS OF PLANTS IS MADE UP OF CARBON.  So, to determine the CARBON accumulation rate for each tree the stand, multiply the BIOMASS accumulation rate by 0.5.

Now calculate the rate of carbon accumulation (in Mg C/ha/yr) for this forest.

Finally, determine how many hectares of forest would be required to balance the carbon emissions by the average car.

How different do you think your answer would be if we did this for an old-growth stand?

This represents a very simple approach to developing a carbon budget for a forest stand.  What major component of the forest (that we ignored) should be incorporated for a more complete analysis? 


WHAT SHOULD YOU TURN IN?  ?  Submit your homework assignment via email directly to me at to the Teaching Assistant for this class Chloe Cason at: THE SUBJECT LINE OF YOUR EMAIL SHOULD INCLUDE THE FOLLOWING TEXT AND NOTHING ELSE!


ESCI325: Homework #2



As an attachment to this email, you should include your Excel worksheet.  Be sure to delete any extra worksheets from this file.  Neatness counts.  In the body of your email message, include the answers to each of the items listed in red above.  You may also include a brief narrative to explain your answers. 


The due date for this assignment is listed on the syllabus.  Assignments that are turned in late will be penalized as described on the class web page.


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Literature Cited

Dixon, R.K., Brown, S., Houghton, R.A., Solomon, A.M., Trexler, M.C. and Wisniewski, J. 1994. Carbon pools and flux of global forest ecosystems. Science 263:185-190.

Grier, C.C. and Logan, R.S. 1977. Old-growth Pseudotsuga menziesii communities of a western Oregon watershed: biomass distribution and production budgets. Ecological Monographs 47:373-400

Harmon, M.E., Franklin, J.F., Swanson, F.J., Sollins, P., Gregory, S.V., Lattin, J.D., Anderson, N.H., Cline, S.P., Aumen, N.G., Sedell, J.R., Lienkaemper, G.W., Cromack, Jr., K. and Cummins, K.W. 1986. Ecology of coarse woody debris in temperate ecosystems. Recent Advances in Ecological Research 15:133-302.

Harmon, M.E., Baker, G.A., Spycher, G. and Greene, S.E. 1990a. Leaf-litter decomposition in the Picea / Tsuga forests of Olympic National Park, Washington, USA. Forest Ecology and Management 31:55-66.

Harmon, M.E., Ferrell, W.K. and Franklin, J.F. 1990b. Effects on carbon storage of conversion of old-growth forests to young forests. Science 247:699-702.

Houghton, R.A. and Woodwell, G.M. 1989. Global climate change. Scientific American 260:36-44.

Houghton, R.A., Callander, B.A. and Varney, S.K. (eds) 1992. Climate Change 1992. Cambridge University Press, Cambridge.

IPCC 1990. Climate Change: The Intergovernmental Panel on Climate Change Scientific Assessment. Houghton, J.T., Jenkins, G.J. and Ephraums, J.J. (eds), Cambridge University Press, Cambridge.

Kauppi, P.E., Mielikainen, K., Kuusela, K. 1992. Biomass and carbon budget of European forests, 1971 to 1990. Science 256:70-74.

Keeling, C.D. 1973. Industrial production of carbon dioxide from fossil fuels and limestone. Tellus 25:174-198.

Orr, J.C. 1993. Accord between ocean models predicting uptake of anthropogenic CO2. Water, Air and Soil Pollution 70:465-482.

Post, W.M., Peng, T.-H., Emanuel, W.R., King, A.W., Dale, V.H. and DeAngelis, D.L. 1990. The global carbon cycle. American Scientist 78:310-326.

Solomon, A.M., Prentice, I.C., Leemans, R. and Cramer, W.P. 1993. The interaction of climate and land use in future terrestrial carbon storage and release. Water, Air and Soil Pollution 70:595-614.

Sundquist, E.T. 1993. The global carbon dioxide budget. Science 259:934-941.

Tans, P.P., Fung, I.Y. and Takahashi, T. 1990. Observational constraints on the global atmospheric CO2 budget. Science 247:1431-1438.

Taylor, J.A. and Lloyd, J. 1992. Sources and sinks of atmospheric CO2 Australian J. Botany 40:407-418.

Waring, R.H. and Franklin, J.F. 1979. Evergreen coniferous forests of the Pacific Northwest. Science 204:1380-1386.

Waring R.H. and Schlesinger, W.H. 1985. Forest Ecosystems: Concepts and Management. Academic Press, New York.