Chapter 14, Problem 4ICA

One of the NAE Grand Challenges for Engineering is Develop Carbon Sequestration Methods Accord1ng to the NAE website “In pre-industrial times, every million molecules of air contained about 280 molocules of carbon dioxide. Today that proportion exceeds 380 molecules per million, and 11 continues to climb. Evidence is mounting that carbon dioxide’s heat-trapping power has already started to boost average global temperatures. If carbon dioxide levels continue upward, further warming could have dire consequences, resulting from rising sea levels, agriculture disruptions and stronger storms (e.g, hurricanes) striking more often·”

The Mauna Loa Carbon Dioxide Record is the longest continuous record of atmospheric concentrations of carbon dioxide (CO₂), the chief greenhouse gas responsible for global climate warming. These data are modeled as the Keeling curve, a graph showing the variation in concentration of atmospheric CO₂ based on measurements taken at the Mauna Loa Observatory in Hawali under the supervision of Charles David Keeling. It is often called the most important geophysical record on Earth and has been instrumental in showing that mankind is changing the composition of the atmosphere through the combustion of fossil fuels.

The Keeling curve also shows a cyclic variation in each year corresponding to the seasonal change in the uptake of CO₂ by the world’s land vegetation. Most of this vegetation is in the northern hemisphere, where most of the land is located. The level decreases from northern spring onward as new plant growth takes CO₂ out of the atmosphere through photosynthesis and rises again in the northern fall as plants and leaves die off and decay to release the gas back into the atmosphere.

Data and wording for this problem set were obtained from www.esrl.noaa.gov/gmd/ccgg/trends/. Additional information on the Mauna Loa Observatory can be found at http://scrippsco2.ucsd.edu/

Note

In the graph, A and Bare not drawn to scale, and the locations of C, D, and E are approximate In other words, you cannot guess the value based upon the graph—you must calculate the value.

Examine the estimated increase in monthly CO₂ emissions for 2019, taken from the Mauna Loa data set. All values given are in parts per million [ppm] CO₂ as the difference between the December 2018 and the monthly 2019 reading.

a. What is the mean of these data?

b. What is the median of these data?

c. The variance of the data set shown here is 5.37 parts per million squared [ppm²]. What is the standard deviation of these data?

d. The estimated annual growth rates for Mauna Loa are close, but not identical to the global growth rates. The standard deviation of the differences is 0.76 parts per millon per year [ppm/year]. What is the variance?