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Tag Archives: ice

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 does climate change impact the spin axis of the planet?

Source: NASA

NASA’s Vital Signs of the planet post, Scientists ID three causes of Earth’s spin axis drift (9/19/18) explains changes in the spin axis.

Earth is not a perfect sphere. When it rotates on its spin axis — an imaginary line that passes through the North and South Poles — it drifts and wobbles. These spin-axis movements are scientifically referred to as “polar motion.” Measurements for the 20th century show that the spin axis drifted about 4 inches (10 centimeters) per year. Over the course of a century, that becomes more than 11 yards (10 meters).

In general, the redistribution of mass on and within Earth — like changes to land, ice sheets, oceans and mantle flow — affects the planet’s rotation. As temperatures increased throughout the 20th century, Greenland’s ice mass decreased. In fact, a total of about 7,500 gigatons — the weight of more than 20 million Empire State Buildings — of Greenland’s ice melted into the ocean during this time period. This makes Greenland one of the top contributors of mass being transferred to the oceans, causing sea level to rise and, consequently, a drift in Earth’s spin axis.

The article explains why the Greenland Ice sheet has such an impact. NASA has also produced an interactive simulation on how different processes contribute to the wobble. There could be a nice vector calculus, linear algebra, or geometry exercises here.

How has Arctic sea ice volume changed?

The Guardian article Arctic’s strongest sea ice breaks up for first time on record by Jonathan Watts (8/21/18) includes an animated graph of Arctic sea ice volume by year. We produce a similar graph using monthly average ice volume from PIOMAS (source cited for the data in the article).  The graph clearly displays the change of ice throughout the year and the loss of ice throughout the years.

Freakish Arctic temperatures have alarmed climate scientists since the beginning of the year. During the sunless winter, a heatwave raised concerns that the polar vortex may be eroding.

This includes the Gulf Stream, which is at its weakest level in 1,600 years due to melting Greenland ice and ocean warming. With lower circulation of water and air, weather systems tend to linger longer.

A dormant hot front has been blamed for record temperatures in Lapland and forest fires in Siberia, much of Scandinavia and elsewhere in the Arctic circle.

The data from PIOMA includes monthly and daily ice volumes.  The R script and csv file that produced the graph here can be downloaded.

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.

How old is Arctic sea ice?

From the NYT: In the Arctic, the Old Ice Is Disappearing

The NYT article In the Arctic, the Old Ice Is Disappearing by Jeremy White and kendra Pierre-Louis (5/14/2018) notes

In the Arctic Ocean, some ice stays frozen year-round, lasting for many years before melting. But this winter, the region hit a record low for ice older than five years.

In fact, in March of 1984 5+ year old ice made up about 70% of all ice and now it makes up only a few percent. There is also less ice overall.

If you really want to explore changes in the age of  Arctic ice go to the NSIDC Satellite Observations of Arctic Change interactive graph.  You can choose a year from 1985 through 2916, see a map of the ice, a bar chart of ice by month by age, and have the graph animate through the months of the year. The differences over the years is extreme. You can get related data from the EASE-Grid Sea Ice Age, Version 3 page, although you will have to register.

What is the state of Arctic Sea Ice?

We are within about a month of the peak of Arctic sea ice in its yearly cycle of freezing and thawing. At the moment, sea ice is at a record low (see chart) tracking close to 2017 and 2016, where as 2012 holds the record for the lowest extent of ice. NSID has an interactive real time chart (the last data point here is Feb 25) where you can select any and all years from 1979 to the present and download the graph. The data can be downloaded in an Excel spreadsheet from their Sea Ice Data and Analysis Tools page where they also have links to animations.  There are materials in both the Calculus Projects and Statistics Projects pages using this data.

What is the connection between Greenland and the East Coast of the U.S.?

In NASA’s post, Greenland melt speeds East Coast sea level rise, they explain:

The recent work reveals a substantial acceleration in sea level rise, roughly from Philadelphia south, starting in the late 20th century. And it is likely a strong confirmation of sea-level “fingerprints,” one of the most counter-intuitive effects of large-scale melting: As ice vanishes, the loss of its gravitational pull lowers sea level nearby, even as sea level rises farther away.

Their analysis shows that the Greenland and Antarctic influence alone would account for an increase in the rate of sea level rise on the East Coast of 0.0016 to 0.0059 inches (0.04 to 0.15 millimeters) each year, varying by location. That’s equivalent to 7.8 inches (0.2 meters) of sea-level rise on the northern East Coast over the next century, and 2.5 feet (0.75 meters) in the south, though the estimates are quantitative and not an attempt at an actual projection.

Emphasis here in increase as this is in addition to the increases based on the meted water and thermal expansion of the water. Connected to this article, is the graph here, change in Greenland ice in Gt, which is from NASA’s Greenland page where you can also get the data.

How can we investigate snow cover?

NOAA has a page, Sea Ice and Snow Cover Extent, where you can create graphs for snow cover by four regions (Northern Hemisphere, North America and Greenland, Eurasia, and North America) for each month of the year. For example the graph here is for North America in March. The green line is the average and the red the trend. For each graph you can download the associated data or simply download the graph.

What are Arctic Winter Warming Events?


From NASA’s Vital Signs of the Planet feature, Arctic winter warming events becoming more frequent, longer-lasting, we learn

Arctic winter warming events – winter days where temperatures peak above 14 degrees Fahrenheit (minus 10 degrees Celsius) – are a normal part of the climate over the ice-covered Arctic Ocean. But new research by an international team that includes NASA scientists finds these events are becoming more frequent and lasting longer than they did three decades ago.

and why does this matter?

Storms that bring warm air to the Arctic not only prevent new ice from forming, but can also break up ice cover that is already present, Graham said. He added that the snowfall from storms also insulates current ice from the cold atmosphere that returns to the Arctic after the cyclones, which can further reduce ice growth.

We know that reduced ice changes albedo, creating a feedback loop (see the Arctic Ice and Global Warming post). The NASA article is from the paper Increasing frequency and duration of Arctic winter warming events where the graph here originates (see supporting information pdf). The data is hard to track down but if you email the authors they may provide you the data used to create these graphs, especially if you mention you want to use it for a linear regression project in a class.

Greenland Ice, Changing Albedo, and a Feedback Loop

The BBC reports: Sea Level Fears as Greenland Darkens. The article discusses a possible feedback loop where as temperatures warm algae growth may flourish, which darkens the surface and changes the albedo to increase melting.

One concern now is that rising temperatures will allow algae to flourish not only on the slopes of the narrow margins of the ice-sheet but also on the flat areas in the far larger interior where melting could happen on a much bigger scale.

We joined the latest phase of research in which scientists set up camp on the ice-sheet to gather accurate measurements of the “albedo” or the amount of solar radiation reflected by the surface.

White snow reflects up to 90% of solar radiation while dark patches of algae will only reflect about 35% or even as little as 1% in the blackest spots.

Other highlights from the article include:

Currently the Greenland ice sheet is adding up to 1mm a year to the rise in the global average level of the oceans.

It is the largest mass of ice in the northern hemisphere covering an area about seven times the size of the United Kingdom and reaching up to 3km (2 miles) in thickness.

This means that the average sea level would rise around the world by about seven metres, more than 20ft, if it all melted.

You can get Greenland Ice Data from NASA’s Vital Signs of the Planet page as noted in a past post.