A Global Warming Primer

The Discovery Channel has an interesting series of videos about the effects of global warming on: polar bears; the Antarctic Ice Sheets; the Amazon rainforest; and the Great Barrier Reef. They also have a nice bit on what goes into the average American carbon footprint.

Natural Selection and Polar vs. Grizzly Bears

What I end up seeing, in this quintessentially 21st century creature, is a glimpse of the future.

— Gamble (2012): One, two, three, er…many. in The Last Word on Nothing.

The effect of rapid Arctic warming on polar bears has been a theme this year in Environmental Science, so this article on the hybridization of polar bears and grizzly bears caught my eye.

As caribou migration routes have moved North, grizzlies have followed and started mating with polar bears. Not only have they produced hybrid young, but those young are fertile. Polar bears and grizzlies only diverged about 150,000 years ago and haven’t developed many genetic differences, despite quite dramatic visual dissimilarities. Second-generation hybrids have now been confirmed in the wild.

This article is also of note to my Middle School science class because we’ve talked about speciation — the divergent evolution of two populations into separate species — before when we looked at the phylogenetic tree and bison evolution in particular. This seems to be a re-convergence after separation. As the climate warms the grizzly bears are able to range further north, while the polar bears are more restricted to the shores by the melted sea ice, so the two populations encounter each other more and more. Thus polar bears, may eventually disappear as they are re-incorporated into the grizzly population.

The author, Jessa Gamble, thinks this is a glimpse of things to come.

The Dish.

Warming of the West Antarctic Ice Sheet

… a breakup of the ice sheet, … could raise global sea levels by 10 feet, possibly more.

— Gillis (2012): Scientists Report Faster Warming in Antarctica in The New York Times.

In an excellent article, Justin Gillis highlights a new paper that shows the West Antarctic Ice sheet to be one of the fastest warming places on Earth.

The black star shows the Byrd Station. The colors show the number of melting days over Antarctica in January 2005. This number increases with warming temperatures (image from supplementary material in Bromwich et al., 2012).

Note to math students: The scientists use linear regression to get the rate of temperature increase.

The record reveals a linear increase in annual temperature between 1958 and 2010 by 2.4±1.2 °C, establishing central West Antarctica as one of the fastest-warming regions globally.

— Bromwich et al., (2012): Central West Antarctica among the most rapidly warming regions on Earth in Nature.

Analyzing the 20th Century Carbon Dioxide Rise: A pre-calculus assignment

Carbon dioxide concentration (ppm) measured at the Mona Loa observatory in Hawaii shows exponential growth and a periodic annual variation.

The carbon dioxide concentration record from Mona Loa in Hawaii is an excellent data set to work with in high-school mathematics classes for two key reasons.

The first has to do with the spark-the-imagination excitement that comes from being able to work with a live, real, scientific record (updated every month) that is so easy to grab (from Scrippts), and is extremely relavant given all the issues we’re dealing with regarding global climate change.

The second is that the data is very clearly the sum of two different types of functions. The exponential growth of CO2 concentration in the atmosphere over the last 60 years dominates, but does not swamp, the annual sinusoidal variability as local plants respond to the seasons.

Assignment

So here’s the assignment using the dataset (mona-loa-2012.xls or plain text mona-loa-2012.csv):

1. Identify the exponential growth function:

Add an exponential curve trendline in a spreadsheet program or manual regression. If using the regression (which I’ve found gives the best match) your equation should have the form:

 y = a b^{cx} + d

while the built-in exponential trendline will usually give something simpler like:

 y = a e^{bx}

2. Subtract the exponential function.

Put the exponential function (model) into your spreadsheet program and subtract it from data set. The result should be just the annual sinusoidal function.

Dataset with the exponential curve subtracted.

If you look carefully you might also see what looks like a longer wavelength periodicity overlain on top of the annual cycle. You can attempt to extract if you wish.

3. Decipher the annual sinusoidal function

Try to match the stripped dataset with a sinusoidal function of the form:

 y = a \sin (bx+c) + d

A good place to start at finding the best-fit coefficients is by recognizing that:

  • a = amplitude;
  • b = frequency (which is the inverse of the wavelength;
  • c = phase (to shift the curve left or right); and
  • d = vertical offset (this sets the baseline of the curve.

Wrap up

Now you have a model for carbon dioxide concentration, so you should be able to predict, for example, what the concentration will be for each month in the years 2020, 2050 and 2100 if the trends continue as they have for the last 60 years. This is the first step in predicting annual temperatures based on increasing CO2 concentrations.

Drought on the Mississippi

Last summer’s drought, and more weather extremes probably due to large-scale global climate change, is having dire effects on shipping on the Mississippi River. Suzanne Goldenberg has an excellent article in the Guardian.

Students look upstream at the Missouri River from the Melvin Price lock and dam, just north of St. Louis, and close to its confluence with the Mississippi River. The dam is tasked with maintaining about 9ft of water in the river for shipping.

Shipping companies say the economic consequences of a shutdown on the Mississippi would be devastating. About $7bn (£4.3bn) in vital commodities – typically grain, coal, heating oil, and cement – moves on the river at this time of year. Cutting off the transport route would have an impact across the mid-west and beyond.

Farmers in the area lost up to three-quarters of their corn and soya bean crops to this year’s drought. … Now, however, [they] are facing the prospect of not being able to sell their grain at all because they can’t get it to market. The farmers may also struggle to find other bulk items, such as fertiliser, that are typically shipped by barge.

— Goldenberg (2012): Mississippi river faces shipping freeze as water levels drop in The Guardian.

The proposed solution is to release more water from the Missouri, however there would be a steep price to pay.

The shipping industry in St Louis wants the White House to order the release of more water from the Missouri river, which flows into the Mississippi, to keep waters high enough for the long barges to float down the river to New Orleans.

Sending out more water from the Missouri would doom states upstream, such as Montana, Nebraska, and South Dakota, which depend on water from the Missouri and are also caught in the drought.

“There are farmers and ranchers up there with livestock that don’t have water to stay alive. They don’t have enough fodder. They don’t have enough irrigation water,” said Robert Criss, a hydrologist at Washington University in St Louis, who has spent his career studying the Mississippi. “What a dumb way to use water during a drought.”

Semi-artificial Selection?

Just like drug resistant germs (we’ve discussed earlier), the rats are evolving.

“They’ve also mutated genetically and are bred to be immune to standard poisons.

“We have had to start using different methods such as trapping and gassing, which can be less effective and more costly.”

–Graham Chappell, from Rapid Pest Control in Newbury in Rowley (2012): Home counties demand stronger poison to deal with mutant ‘super rats’ in The Telegraph.

$10.09 per ton of Carbon Dioxide

… one metric ton of carbon dioxide is what’s produced by an average month of electricity use in a U.S. home.

Troeh (2012): California’s first carbon auction launches pollution market on Marketplace.

California recently auctioned off a set of carbon emission permits as the start of an effort to reduce emissions of greenhouse gasses with an emissions trading system.

The first 23.1 million permits sold out at $10.09 per ton.

Eve Troeh discusses: