Mathematics for Sustainability
measuring, flowing, networking, changing, risking, deciding
A couple of exercises for chapter 5 refer to a dataset of Arctic sea ice extent, and we also plan to add an online case study on regression to the mean where this will be one of the examples. The data comes from the National Snow and Ice Data Center Arctic Sea Ice News and Analysis. The dataset is more completely summarized in the graphic below.
This page, from the World Bank, gives comprehensive data on worldwide carbon dioxide emissions, broken down in a variety of ways (e.g., country by country).
This dataset is referenced in problem 4 of chapter 5 of the book.
This post is a supplement to the discussion of extreme value statistics at the end of Section 5.3 of the book. You can find an online extreme value distribution calculator, provided by South Dakota State University, at
http://onlinecalc.sdsu.edu/onlinegumbel.php
This calculator fits a Gumbel distribution (a form of generalized extreme value distribution) to a data set. It uses the language of river floods because that is what the authors are interested in, but the underlying mathematics applies to many different situations.
To use the calculator one provides a data series consisting of extreme values. For instance, one might provide the data series
12.1; 11; 2; 1.8; 16.4; 6.7; 8; 3; 4; 9;
which represents the biggest value of some variable (the depth of the deepest flood, the windspeed of the strongest storm, or whatever) in each of 10 successive years. The output of the calculator is a table giving a probability distribution. It has five columns: the key ones are labeled T (return period), P (probability) and Q (“flood discharge” for this calculator, but it refers to whatever variable we are modeling). Here is part of the output for the data series above:
| Return period T, year | Probability P, percent | Value Q |
| 25 | 4 | 21 |
| 50 | 2 | 25 |
| 100 | 1 | 28 |
This tells us (based on the data provided) that, for instance, the value \(Q=28\) will be exceeded only once in a hundred years; the value \(Q=25\) will be exceeded only once in fifty years; and so on.
This is a sample case study
Here is a link to the Washington Post article The world is about to install 700 million air conditioners. Here’s what that means for the climate, which is referenced in one of the Case Study exercises.
The article begins,
As summer temperatures finally settle in, many in the United States take it for granted that they can dial down the thermostat: Americans use 5 percent of all of their electricity cooling homes and buildings. In many other countries, however — including countries in much hotter climates — air conditioning is still a relative rarity. But as these countries boom in wealth and population, and extend electricity to more people even as the climate warms, the projections are clear: They are going to install mind-boggling amounts of air conditioning, not just for comfort but as a health necessity.