MODELING CO2 LEVELS IN THE ATMOSPHERE
The graph above shows the Keeling Curve, which plots CO2 levels in the atmosphere. The data in the
table on the back of this sheet gives the annual average CO2 level for the data starting in 1980.
a. What causes the seasonal fluctuations in the CO2 levels shown in the graph?
b. The underlying normal CO2 level is 280 ppm. Subtract this from each data point to obtain a table of
values for CO2 level above 280 ppm for the years since 1980.
c. For the column of values found in part (b), create another set of values for the ratio of successive
years. Are the ratios relatively constant? What is the average ratio?
d. Your work in part (c) suggests that an exponential curve would be a good fit to the data. Why? Find
an equation for the exponential function that fits the data for CO 2 levels. According to your
equation, what will CO2 concentration reach by 2025? By 2100? When will CO2 levels reach
500ppm?
e. The seasonal oscillations in the Keeling Curve suggest that a sinusoidal curve can be added to the
exponential curve to model this curve. Use the monthly data for the year 2000 to fit a sine curve to
the monthly deviations from the annual average.
f. Combine your exponential and sinusoidal models to obtain a model that fits the overall trend in the
data, including seasonal oscillations.
Jan
369.14
Feb
369.46
Mar
370.52
Apr
371.66
May
371.82
Jun
371.70
Jul
370.12
Aug
368.12
Sep
366.62
Oct
366.73
Nov
368.29
Dec
369.53
TABLE OF VALUES FOR ANNUAL AVERAGE CO2 LEVELS
Year
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
CO2 (ppm)
338.68
340.11
341.22
342.84
344.41
345.87
347.19
348.98
351.45
352.90
354.16
355.48
356.27
356.95
358.64
360.62
362.36
363.47
366.50
368.14
369.40
371.07
373.17
375.78
377.55
379.76
381.85
383.71
385.57
387.35
389.78
391.65
393.84
396.48
CO2 above 280
Ratios