Sources of Greenhouse Emissions
Your Challenge
We have all heard of the importance of carbon dioxide (CO2) as a greenhouse gas. What other gases contribute to global warming? Where do greenhouse gases come from? What is the relative importance of these different sources? Do all greenhouse gases contribute to global warming in the same way? These are some of the topics we will explore in this challenge. Let’s get started.
Process
BASIC LEVEL (1 point) First, let’s collect some data. Using the links below (or others you find yourself!) identify the main types and quantities of greenhouse gases emitted into our atmosphere and indicate how much of each type comes from natural sources versus anthropogenic sources. Also identify the natural and anthropogenic activities that result in the release of these gases into the air. Be sure to cite the source of your information. Display your data graphically using Microsoft Excel or another graphing program. Then use your data to answer the following questions:
 Which gas(es) contribute most to global warming?
 Which human activities contribute to the greatest release of greenhouse gases?
 What is the greatest source of natural greenhouse gases?
 Tell us something new that you learned in the course of studying this data.
http://www.eia.doe.gov/oiaf/1605/ggrpt/index.html http://en.wikipedia.org/wiki/Image:Greenhouse_Gas_by_Sector.png http://globalwarming.enviroweb.org/ishappening/sources/index.html http://www.ace.mmu.ac.uk/resources/gcc/64.html
GOING BEYOND (2 points) Now that you have an idea of the relative amounts and sources of greenhouse gases, let’s dig a little deeper. Each greenhouse gas emits its own electromagnetic wave spectrum; therefore, each gas has its own heatabsorbing/emitting ability and thus not all greenhouse gases contribute to global warming to the same degree. For example, it is known that, per unit mass, methane actually contributes more to global warming (i.e., warming of the atmosphere) than CO2.
So, it is inaccurate to simply look at the amounts of greenhouse gases emitted in trying to identify the biggest global warming “culprit”. We need to be able to measure the actual impact of these gases on global warming as well. Scientists have come up with a way to do this, using a factor called the Global Warming Potential (GWP).
The GWP is a ratio of the degree of warming caused by a greenhouse gas relative to the degree of warming caused by an equivalent amount of CO2. If we knew that the GWP for methane was 4, for example, that would tell us that, for equivalent masses of methane and CO2, methane has four times the impact on global warming than CO2. Therefore, a ton of methane would be equivalent to 4 tons of CO2 in terms of its effect on global warming. This is really important for scientists and policy makers to know in the design of any plan that addresses global warming.
The GWP is dependent not only on the radiative efficiency of a gas relative to that of carbon dioxide, but also on its decay rate (the amount removed from the atmosphere over time due to any number of processes) relative to that of carbon dioxide. Let’s think about this last point for a second. Compounds in our atmosphere don’t hang out there forever. They can, for example, be chemically transformed through reactions with other compounds (as in the way methane is removed when it reacts with hydroxyl radicals in the air) or physically removed (as in the way CO2 is pulled from the atmosphere by plants through photosynthesis). If you have two gases that have the same radiative efficiency, the one with the longer atmospheric “life” will have a greater impact on global warming, simply because it is around longer. Therefore, a GWP must be calculated over a specific time interval, which must be stated whenever a GWP is quoted or else the value is meaningless.
Now that you have an understanding of GWP, here is your challenge. Using the links below, find the GWP for each greenhouse gas you identified in the Basic Level challenge (be sure to state the time period used in its calculation!). Now correct your data from the Basic Level challenge by multiplying each of the greenhouse gas quantities by their respective GWP. When you are done, you will be able to directly compare the relative importance of the greenhouse gases and their sources. As you did in the Basic Level challenge, present your revised data graphically. Has this analysis changed the way you might have been thinking about the global warming problem? Prepare a paragraph about your observations.
http://www.eia.doe.gov/oiaf/1605/gwp.html http://en.wikipedia.org/wiki/Global_warming_potential http://www.grida.no/climate/ipcc_tar/wg1/247.htm http://unfccc.int/ghg_emissions_data/items/3800.php
GOING CRAZY (3 points) In this challenge, we’ll explore the GWP even further! The equation used to calculate the GWP is:
where:
 x = the greenhouse gas of interest
 TH = the time period over which the calculation is considered
 ax = the radiative efficiency due to a unit increase in atmospheric abundance of the substance (i.e., Wm2 kg1)
 [x(t)] = the timedependent decay in abundance of the substance following an instantaneous release of it at time t=0
 dt = time interval (d stands for “delta”, which is the Greek symbol _, and is used in mathematics to mean a small or incremental change)
(The denominator contains the corresponding quantities for CO2, where “r” refers to “reference gas”. Dividing through by this quantity “normalizes” the value so that all GWPs are referenced to CO2.)
For many of you, this will be the first time you have seen an equation of this form. Don’t be daunted! It is called an integral, which is represented by the symbol “∫”. In very simple terms, an integral is the total quantity of something (e.g. area, mass, volume) that might be varying over some other quantity (typically time or distance). The GWP, for example, changes over time because the quantity of a given greenhouse gas in the atmosphere varies with time. The goal of this challenge is to understand how integration can be used to calculate such a quantity!
To do this, we will break up our discussion into four simple steps. The first step will give you the basic idea behind integration. The second will provide you with an example to consider. In the third step, you will have a chance to integrate an expression numerically, which is a method of approximating a real integral. And in the fourth step, we will relate the “numerical” integration approach you performed to approximate your answer to calculus integration, which allows the exact quantity to be determined. Don’t worry that integration is the subject of calculus – we’re going to work on understanding just the basic ideas. Here we go!
Part 1 – The Basic Idea
The integral was originally developed, in part, to compute the area of a shape for which geometry formulas (e.g. circles, regular polygons, triangles) were not available. For example, we know how to calculate the area of this shape:
But, how do we figure out the area of this one?
The basic idea is quite easy to understand. Simply break up the shape into small regular shapes (subintervals) that approximate a rectangle and then add them all up! Your answer won’t be perfect, but it will be close. The smaller your subinterval, the better your approximation. You should be able to visually see this in the examples below.
Few Subintervals
Many Subintervals
That’s it for Part 1. Let’s look at an example.
Part 2 – The Integration Example f(x) = 2x
Let’s say we have a graph of f(x) = 2x, which is simply the equation for a straight line that goes through the origin. By using this simple example, we can compare the “approximation approach” we introduced in Part 1 to the exact answer. Before we start, let’s try to add a little meaning to the numbers, so imagine that you have been measuring the emission rate of CO2 into the atmosphere over time and you find that your data follows a line that can be represented by the equation f(x)=2x (remember, this is for the sake of our discussion here; in reality, actual CO2 emissions in the atmosphere do not follow this equation). Here is the graph, and you can see that it tells us at any time, the rate at which CO2 is being added to the atmosphere.
Now, let’s say that we want to know how much CO2 has actually gotten into the atmosphere over a certain period of time, say between 0 and 5 years. This would, simply be the rate times the time interval, if the rate was constant, but our rate is changing over time. So, to do this using a numerical integration approach, we need to approximate the relevant portion of our graph (from 0 to 5 years) with small rectangles. Let’s use subintervals of one year.
To do the calculation manually can be a bit tedious, especially if you are working with many subintervals. Here’s what the calculations look like and it should be selfexplanatory. If you have any trouble understanding them, be sure to contact your mentor!
Subinterval (dx = 1 year) 
x (years) 
f(x) = 2x (tons CO_{2}/year) 
f(x) * dx (tons CO_{2}) 
1 
1 
2 
2 
2 
2 
4 
4 
3 
3 
6 
6 
4 
4 
8 
8 
5 
5 
10 
10 




Total CO_{2} Emission (tons) 


30 
Because the “shape” of our figure is a geometrically easy one, we can calculate the actual area under the “curve” by using the formula for a triangle. Doing so, yields:
Area of triangle from 0 years to 5 years
= _ baseheight
= _5 years10 tons CO2/year
= 25 tons CO2
Note how similar these two answers are. Once again, had we used a smaller subinterval, we would have approximated the solution even better.
Part 3 – The Integration Challenge f(x) = x2
And here we are, ready for the integration challenge. Let’s say that instead of the linear relationship between rate of CO2 emission and time, you identified a power relationship of the form f(x) = x3. Your task is to figure out the amount of CO2 released between 0 and 5 years, using the numerical integration technique you learned in Part 2. Use a graphing program such as Microsoft Excel or the link provided below to plot this relationship. Then structure a table that shows your calculations. Perform this calculation twice; once with a dx of 1 year and again with a dx of 0.5 years. Good luck!
http://people.hofstra.edu/staff/steven_r_costenoble/Graf/Graf.html
Part 4 – Relating Numerical Integration to Calculus Integration
You have observed that your approximation of the area under the curve becomes more exact as you increase the number of subintervals. If you could partition your area into an infinite number of subintervals, you would obtain the exact area under the curve. This is denoted by the following symbol, which is read as “the integral from a to b of f(x)”.
∫ab f(x)
In calculus, techniques are given for evaluating integrals to obtain exact answers.