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Tag Archives: calculus

How do we take the temperature of the oceans?

APO is atmospheric potential oxygen.

The recent BBC article Climate change: Oceans ‘soaking up more heat than estimated’  b

The key element is the fact that as waters get warmer they release more carbon dioxide and oxygen into the air.

“When the ocean warms, the amount of these gases that the ocean is able to hold goes down,” said Dr Resplandy.

“So what we measured was the amount lost by the oceans, and then we can calculate how much warming we need to explain that change in gases.”

The image here is copied from the original article in Nature, Quantification of ocean heat uptake from changes in atmospheric O2 and COcomposition by Resplandy et. el (10/31/18) . The abstract to the paper provides a nice summary:

The ocean is the main source of thermal inertia in the climate system1. During recent decades, ocean heat uptake has been quantified by using hydrographic temperature measurements and data from the Argo float program, which expanded its coverage after 20072,3. However, these estimates all use the same imperfect ocean dataset and share additional uncertainties resulting from sparse coverage, especially before 20074,5. Here we provide an independent estimate by using measurements of atmospheric oxygen (O2) and carbon dioxide (CO2)—levels of which increase as the ocean warms and releases gases—as a whole-ocean thermometer. We show that the ocean gained 1.33 ± 0.20  × 1022 joules of heat per year between 1991 and 2016, equivalent to a planetary energy imbalance of 0.83 ± 0.11 watts per square metre of Earth’s surface. We also find that the ocean-warming effect that led to the outgassing of O2 and CO2 can be isolated from the direct effects of anthropogenic emissions and CO2 sinks. Our result—which relies on high-precision O2 measurements dating back to 19916—suggests that ocean warming is at the high end of previous estimates, with implications for policy-relevant measurements of the Earth response to climate change, such as climate sensitivity to greenhouse gases7 and the thermal component of sea-level rise8.

The paper has other interesting graphs that could be used in a QL based class. For a calculus class, the graph here is an example of the use of the Δx notation in the “real world”.

How are climatic zones changing?

The Yale Environment 360 article Redrawing the Map: How the World’s Climate Zones Are Shifting  by Nicola Jones (10/23/18)  provides animated maps, such as the one below, and quantitative statements about changing ecology including rates (great for a calculus class):

Lauren Parker and John Abatzoglou of the University of Idaho tracked what would happen to hardiness zones from 2041 to 2070 under future global warming scenarios, and found the lines will continue to march northward at a “climate velocity” of 13.3 miles per decade.

One study in northern Canada found that the permafrost around James Bay had retreated 80 miles north over 50 years. Studies of ground temperatures in boreholes have also revealed frightening rates of change, says Schafer. “What we’re seeing is 20 meters down, it’s increasing as high as 1-2 degrees C per decade,” he says. “In the permafrost world that’s a really rapid change. Extremely rapid.”

North America is seeing the opposite phenomenon: Its arable land is romping northward, expanding the wheat belt into higher and higher latitudes. Scientists project it could go from about 55 degrees north today to as much as 65 degrees North — the latitude of Fairbanks, Alaska — by 2050. That’s about 160 miles per decade.

The article includes potential ramifications of these changes along with other quantitative information.

Graphic: Hardiness zones in the U.S., which track average low temperatures in winter, have all shifted northward by half a zone warmer since 1990. SOURCE: UNITED STATES DEPARTMENT OF AGRICULTURE. GRAPHIC BY KATIE PEEK.

How well do we understand rising sea levels?

An ice-choked fjord in Greenland. Image credit: NASA/JPL-Caltech.

NASA’s Vital Signs of the Planet feature,  Keeping score on Earth’s rising seas by Pat Brennan (9/1918) summarizes a recent paper that  “ ‘closes’ the sea-level budget to within 0.3 millimeters of sea-level rise per year since 1993.”

A just-published paper assembles virtually all the puzzle pieces – melting ice, warming and expanding waters, sinking coastlines and a stew of other factors – to arrive at a picture of remarkable precision. Since 1993, global sea level has been rising by an average 3.1 millimeters per year, with the rise accelerating by 0.1 millimeter per year, according to the study published Aug. 28 in the journal, “Earth System Science Data.”

“Global mean sea level is not rising linearly, as has been thought before,” said lead author Anny Cazenave of France’s Laboratory for Studies in Geophysics and Oceanography (LEGOS). “We now know it is clearly accelerating.”

The above paragraphs can be used as calculus in the news and sea level data is available from NASA’s Sea Level page.

How fast is Antarctica melting (and a quick calculus project)?

A recent NYT article, Antarctica Is Melting Three Times as Fast as a Decade Ago by Kendra Pierre-Louis (6/13/2018), states clearly that Antarctica is melting, well, three times faster than a decade ago, which is a rate of change statement. Rapid melting should cause some concern since:

Between 60 and 90 percent of the world’s fresh water is frozen in the ice sheets of Antarctica, a continent roughly the size of the United States and Mexico combined. If all that ice melted, it would be enough to raise the world’s sea levels by roughly 200 feet.

Any calculus student can roughly check the melting statement.  Antarctica ice data is available at NASA’s Vital Signs of the Planet Ice Sheets page. There you can download change in Antarctica ice sheet data since 2002. (Note: The NYT article has a graph going back to 1992, but ends in 2017 as does the NASA data.) A quick scatter plot and a regression line shows that the change is not linear and the data set is concave down. (The graph here is the NASA data and produces in R – the Calculus Projects page now has some R scripts for those interested.)  Now, a quadratic fit to the data followed by a derivative yields that in 2007 the Antarctica was losing 95 gigatonnes of ice per year and in 2017 it was 195.6 gigatonnes per year. Even with this quick simple method melting has more than doubled from 2007 to 2017. The NYT article states:

While that won’t happen overnight, Antarctica is indeed melting, and a study published Wednesday in the journal Nature shows that the melting is speeding up.

This is an excellent sentence to analyze from a calculus perspective. Given that the current trend in the data is not linear and at least about quadratic, then melting is going to increase each year.  On the other hand, maybe they are trying to suggest that melting is increasing more than expected under past trends, for example the fit to the data is more cubic than quadratic. In other words, is the derivative of ice loss linear or something else? If everyone knew calculus the changes in the rate of ice loss could be stated precisely.