Sustainability Math A Quantitative Literacy and Mathematics Resource for Instructors

The energy flow diagram here is from the EIA and represents 2016 petroleum use in millions of barrels per day. For example, the U.S. used 13.88 million barrels of petroleum per day for transportation in 2016. The EIA energy flow diagrams (found on the right sidebar) are excellent for use in the classroom and they have recently been updated with 2016 data. They produce flow diagrams for total energy, petroleum, natural gas, coal, and electricity as well as a sources and sectors chart. They keep an archive of their charts dating back to 1996.

Thanks to the folks at the NASA Scientific Visualization Studio for this visualization of Annual Arctic Sea Ice Minimum 1979-2015 with Area Graph (click on the visual to play). Arctic ice data is available in the calculus and statistics sections. A recent Economist article The thawing Arctic threatens an environmental catastrophe adds some context.

The Arctic has been warming at twice the rate of the rest of the world for decades because of feedback loops that have reduced the albedo effect, a measure of the way Earth reflects heat. Unlike the rest of the planet the polar regions release more heat into space than they absorb, in effect cooling the planet, because sunlight is reflected by ice and snow. When it is replaced by water or dark ground, more heat is retained. That is precisely what is happening in the Arctic’s defrosting landscape.

This blog has already noted a the feedback loop from melting permafrost, Methane Bubbles – A Feedback Loop. A recent BBC article, There Are Diseases Hidden In Ice And They Are Waking Up – Long-dormant bacteria and viruses, trapped in ice and permafrost for centuries, are reviving as Earth’s climate warms, is a well referenced article about the possible consequences of melting permafrost (picture from the article with caption: Bacteria have been found dormant in Antarctic ice (Credit: Colin Harris/Era Images/Alamy)).

“Permafrost is a very good preserver of microbes and viruses, because it is cold, there is no oxygen, and it is dark,” says evolutionary biologist Jean-Michel Claverie at Aix-Marseille University in France. “Pathogenic viruses that can infect humans or animals might be preserved in old permafrost layers, including some that have caused global epidemics in the past.”

If you are incorporating climate change issues in the classroom then the article provides for excellent classroom discussions with interesting science. The article concludes:

How much should we be concerned about all this?

One argument is that the risk from permafrost pathogens is inherently unknowable, so they should not overtly concern us. Instead, we should focus on more established threats from climate change. For instance, as Earth warms northern countries will become more susceptible to outbreaks of “southern” diseases like malaria, cholera and dengue fever, as these pathogens thrive at warmer temperatures.

The alternative perspective is that we should not ignore risks just because we cannot quantify them.

“Following our work and that of others, there is now a non-zero probability that pathogenic microbes could be revived, and infect us,” says Claverie. “How likely that is is not known, but it’s a possibility. It could be bacteria that are curable with antibiotics, or resistant bacteria, or a virus. If the pathogen hasn’t been in contact with humans for a long time, then our immune system would not be prepared. So yes, that could be dangerous.”

It would be nice if these articles discussed the populations most at risk. It is often the case that those of lower socioeconomic status are more vulnerable.  Many issues related to climate change have both a social justice component, as well as an ethical question related to the fact that those that contribute little to climate change are often impacted disproportionately.

A few posts ago I posted about Vital Signs of the Planet from NASA as place for graphs and data. I also recently noted the NASA Scientific Visualization Studio. Putting the two together here is a visualization of changes of Greenland Ice (click anywhere to play) and again you can get the data from NASA’s Vital Signs of the Planet.

Stats classes are always looking for interesting data. One place to look in YouGov. For example, they did a poll (Note: it is not clear how the sample was obtained but they do provide a sample size.) asking people if life is fair.  Here are the results by gender.

1. Do you think life is fair or not fair?

You are set for a statistical test comparing Male vs Female perception of life being fair or not. This now allows for a discussion of why women would respond differently than men. One extra bonus on the site is you can look at the same questions broken down by other categories including income. Go to the YouGov Results page to see the data they have.

The crack in the Larsen C ice shelf has been in the news recently. For instance Newsweek’s Another Huge Crack has Appeared on the Antarctica’s Larsen C Ice Shelf or the BBC’s The Crack that is Redrawing the World’s Map. Both articles seem to stem from the Project Midas news release A new branch of the rift on Larsen C (they made the map here).  The Newsweek article notes:

Current projections indicate that if the Larsen C ice shelf disintegrates, it could raise sea levels by up to 10cm.

A NASA report, Breaking the ice: Antarctic rifts and future sea level is a little more precise:

Yet even if the whole ice shelf were to break up, Fricker said, the resulting sea level rise would be minimal. The glaciers held back by the shelf are not so imposing.

“The Larsen C ice shelf only holds back about one centimeter of global sea level rise,” she said.

Still, the crack in Larsen C could be a bellwether for ice shelves elsewhere on the continent, Rignot said.

“What we are seeing on Larsen C has implications for the big ice shelves farther south that hold considerable (sea level) potential,” he said. The loss of these larger ice shelves and the resulting acceleration of glacial calving could amount to meters of sea level rise in the decades and centuries to come.

The NASA article does provide some balance:

Ice shelf demise, or business as usual?

The crack could be the start of a period of sustained retreat, similar to what happened to Larsen B, said Ala Khazendar, a JPL scientist who has investigated both Larsen B and Larsen C. An increasingly weakened ice shelf allows glaciers to speed their flow into the ocean, and the shelf, unable to recover its former bulk and solidity, disintegrates.

Or, this could turn out to be a normal calving episode.

“We have no way yet of knowing whether Larsen C is doing what Larsen C has been doing for thousands of years, or whether we are witnessing the beginning of the end of Larsen C,” he said.

If you are talking about climate change in the classroom, the NASA article is excellent for further readings and discussion as well as the Project Midas site. There is some interesting science here in understanding ice.

Vital Signs of the Planet from NASA is a place for graphs and data. The graph here is change in the mass of the Greenland Ice Sheet. On the Land Ice page there is also a graph of changes in the Antarctica Ice. Underneath each graph is a link to data (HTTP), which will give you data for both Greenland and Antarctica ice as well as sea level change. All three sets can be used for linear regression or multiple regression predicting sea level change based on both ice mass changes (recall that melting sea ice doesn’t raise sea levels but land ice does).

This move is from NOAA and embedded in their page Trends in Atmospheric Carbon Dioxide where you can download a full resolution version of this animation. There is a lot of information in this video and simply reading the information could be a challenge for students.

A NOAA news report, Global Climate Report – March 2017 Monthly temperature anomalies versus El Niño, provides us with the graph here of monthly temperature colored coded by ENSO events. The report notes that

March 2017 marks the first time since April 2016 that the global land and ocean temperature departure from average is greater than 1.0°C (1.8°F).

This is also the first time a monthly temperature departure from average surpasses 1.0°C (1.8°F) in the absence of an El Niño episode in the tropical Pacific Ocean.

March 2017 tied with January 2016 as the fifth highest monthly global land and ocean temperature departure from average on record (1,647 monthly records).

According to the NOAA report Carbon dioxide levels rose at record pace for 2nd straight year (graph here from their report).

“The rate of CO₂ growth over the last decade is 100 to 200 times faster than what the Earth experienced during the transition from the last Ice Age,” Tans said. “This is a real shock to the atmosphere.”

Globally averaged CO₂ levels passed 400 ppm in 2015 — a 43-percent increase over pre-industrial levels. In February 2017, CO₂ levels at Mauna Loa had already climbed to 406.42 ppm.

NOAA provides an interactive website with data: Trends in Atmospheric Carbon Dioxide. The calculus materials page here also has Mauna Loa CO2 data and a project.