Instructor's notes.

The model used in the activity " Using mass balance model to understand carbon dioxide" is based on the simple mass balance relation. 

                (eqn. 1)

Where C is the global atmospheric concentration of CO2 (in ppmv), S is the emission source strength (ppm/yr), and t is the atmospheric lifetime (yrs).

The general solution to equation 1 for any arbitrary time dependent emission source S(t) is:

                (eqn. 2)

We have solved equation 2 assuming an emission source strength of the form,

                                (eqn. 3)     [see solution]

An interactive online program has been written in which students can modify the input values ( Co, t, So, and R) and then generate a graph of C vs t.  A table of values for C and S as functions of time is also generated.  Students first "calibrate" the model to fit recent observations and then use the model to explore future emission scenarios.  Although I  have used this assignment after a brief in-class discussion of the model basics and online modeling environment, the two activities below provide a solid background of the mass balance concept and its application to global trace gas concentrations.

For classes with limited mathematics ability, I describe the mathematics of the model using only the finite difference form of equation 1.  Although it is tempting to also discuss Euler's number e, I purposely avoid this for classes with weak math skills as I believe that it adds little (if anything) to their understanding of the mass balance physical processes. 

waterbucket.gif (5811 bytes) To give students a better feel for the model you may want to use some or all of the introductory water bucket model activity at: often use a  2-liter pop bottle, with flow from a sink into the top and a hole in the bottom, as a physical model during an in class discussion of mass balance.  The lifetime for this water bucket model is then related to the hole size in the bottle and viscosity of the water.
Earth4.gif (5423 bytes) The next suggested activity that is useful in bridging the gap between the waterbucket model and its application to the atmosphere is located at:  This site also provides links to basic definition of terms and basic theory in a context of atmospheric science.