Warming, Cooling, and Urban Ozone Pollution

Part 5: Ozone Pollution in Atlanta

We suppose that y = y(t) is the concentration of ozone in parts per million by volume (ppmv), where t is measured in years. Our simulated measurements are taken at a fixed location in Atlanta on the same summer afternoon each year for a decade. We will explore whether the data fit a model of the form

by using symmetric difference quotients to estimate the derivative. If we find the relationship between rate and concentration is linear, then the slope of the line is the negative of k, and b is the y-intercept divided by k. Thus, we can infer the "natural" level of ozone. And, once we know k and b, we can fit a solution function,

from which we can answer such questions as how much AHCs have to be reduced to meet the NAAQS standard.

1. Enter and plot the ozone concentration data. Does the plot look like exponential decay?
2. Compute the slope estimates as symmetric difference quotients. Plot the slopes against the ozone concentrations. Does the relationship appear to be linear?
3. Rather than compute a slope and a y-intercept directly from the data, we will use the built-in least squares fitting routine. Do this now, and use the result to calculate k and b.
4. Enter in your worksheeet a formula for y as a function of t. Plot this model function, and overlay the plot on the plot of the concentration data. How well does it fit?
5. What portion of the original 0.15 ppmv concentration of ozone is attributable to NHCs?
6. Over the 10 years of the study, AHCs were reduced by 30% -- which would have been sufficient to bring Atlanta into compliance with NAAQS if NHCs were not a contributing factor. Assuming no change in levels of nitrogen oxides, and assuming ozone production responds linearly to reduction in AHCs, how much would AHCs have to be reduced to bring Atlanta into compliance with the 0.12 ppmv standard?

---

Send comments to the authors <modules at math.duke.edu>

Last modified: October 21, 1997