1. Mass Balance
for the carbon cycle
Robert MacKay
Clark College and Washington State
University Vancouver, WA

2. Camping

3. Student Learning Goals
 Use a model to estimate the future concentrations of carbon dioxide
under several different assumed emission scenarios.
 Learn how different carbon dioxide emission scenarios influence our
best prediction of future global temperatures.
 Learn how a mass balance model applies to the global atmosphere.
 Calibrate a model with recent observations.
 Understand the sluggishness of the carbon cycle to anthropogenic
changes.
 Synthesize results into a well written summary.
 Accurately read graphical information.
 Read and interpolate data from a table of values.

4. http://serc.carleton.edu/introgeo/mathstatmodels/examples/MassBalance.html
http://serc.carleton.edu/introgeo/teachingwdata/examples/CFCsModel.html
http://serc.carleton.edu/quantskills/activities/co2_global.html

5. From page 212 IPCC “Climate Change 2007 The Physical Science Basis”

6. IPCC 2007 Figure 7.3

7. IPCC 2007 Figure 7.3
The Global Carbon Cycle for the 1990s . Red anthropogenic black preindustrial.
From the diagram above, estimate the fraction of total anthropogenic carbon emissions
that are attributable to land use changes.

8. IPCC 2007 Figure 7.3
The Global Carbon Cycle for the 1990s . Red anthropogenic black preindustrial.
From the diagram above, estimate the fraction of total anthropogenic carbon
emissions that are attributable to land use changes.
1.6/(8.0)=0.20 =20%

9. IPCC 2007 Figure 7.3
The Global Carbon Cycle for the 1990s . Red anthropogenic black preindustrial.
From the diagram above, estimate the fraction of all carbon emitted from human
activity that is still in the atmosphere.

10. IPCC 2007 Figure 7.3
The Global Carbon Cycle for the 1990s . Red anthropogenic black preindustrial.
From the diagram above, estimate the fraction of all carbon emitted from human
activity that is still in the atmosphere.
165/(244+39)=58%

11. Basic Model
What’s missing from
this carbon cycle
model?

12. Basic Model
What’s missing from
this carbon cycle
model?
Rock (Lithosphere)
and Humans

13. [ CO2 ]t +1 = ( A0,t + a0 St ) + ( A1,t e−1 / τ1 + a1 * St ) + ( A2,t e−1 / τ 2 + a2 * St ) + ( A3,t e−1 / τ 3 + a3 * St )
IPCC 2007 page 213
τ 0 = infinite
a0=0.217
a1=0.259 τ 1 =172.9
a2=0.338 τ 2=18.51
a3=0.186 τ 3=1.186
Introduction to multi-box models (lecture notes)
http://www.atmosedu.com/WSU/esrp310-550/notes/BoxModels/MatrixPractice1.pdf
“Normal modes and the transient response of the climate system” , GRL
MacKay and Ko, 1997 (http://www.atmosedu.com/WSU/esrp310-550/OceanModel.pdf )

14. Model and preliminary assignment
 http://www.atmosedu.com/physlets/GlobalPollutio

16. Conclusion
 The model can be used in an interactive lecture
discussion or as an assignment.
 Implements the 2007 IPCC carbon impulse response
function.
 Captures both the fast response and the sluggishness of
the carbon cycle.
 Helps students understand how policy changes today
have limited short term (20 yr) influence but important
long term (60 yr) influence.
 Gives students more practice using graphical
information.
 Open ended questions allow student to think for
themselves.