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Tag Archives: climate change

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 much are the oceans warming?

A year ago Climate Central posted the article Oceans Are Heating Up with a graph of sea surface temperature anomalies while providing context on issues of ocean warming:

 93 percent of the excess heat absorbed by the climate system goes into our oceans, creating major consequences. While more extreme storms and rising sea levels are some of the impacts of warmer oceans, rising CO2 levels and the resulting warmer oceans are impacting ocean health itself. The most well­ known effects are coral bleaching and ocean acidification, but an emerging issue is the decreasing oxygen levels in the warming waters.

The graph here is from NOAA’s Global Ocean Heat and Salt Content page. There you will find numerous updated graphs related to ocean heat content.  For related data go to NOAA’s Basin time series of heat content page to find about 50 time series on ocean heat.

For context on units, a person at rest typically generates about 60 joules of heat per minute while the graph here has y-axis units of 10^22 Joules.

What is the state of the Rio Grande?

The NYT article, In a Warming West – the Rio Grande Is Drying Up by Henry Fountain (5/24/2018) answers the question.

Even in a good year, much of the Rio Grande is diverted for irrigation. But it’s only May, and the river is already turning to sand.

“The effect of long-term warming is to make it harder to count on snowmelt runoff in wet times,” said David S. Gutzler, a climate scientist at the University of New Mexico. “And it makes the dry times much harder than they used to be.”

With spring runoff about one-sixth of average and more than 90 percent of New Mexico in severe to exceptional drought, conditions here are extreme. Even in wetter years long stretches of the riverbed eventually dry as water is diverted to farmers, but this year the drying began a couple of months earlier than usual. Some people are concerned that it may dry as far as Albuquerque, 75 miles north.

What the article is missing is data. For example, we have here a graph of daily discharge in cubic feet per second at the Albuquerque station (directions below on how to obtain this graph and associated data.).  Note, that the graph is on a log scale and so is there is downward trend in this data?  Since 1991, the Rio Grande hasn’t stopped flowing in Albuquerque, although is came close around 2014.  Other stations farther south have periods of zero discharge. Use the directions below to explore water flow of the Rio Grande at several locations.  The data is naturally collected as a rate and so it is interesting for calculus classes as well as statistics classes.

To obtain water flow data at any USGS station around the country start at the National Water Information System: Mapper (Note: Different sites around the country will have different dates and type of data available.) Click on any of the sites to get a window with a link to access the data.  The graph here comes from selecting the USGS 08330000 RIO GRANDE AT ALBUQUERQUE, NM station. On that page under Available data for this site  select Time series: Current/Historical observations. For this specific graph we selected a time frame for the whole data set and selected Graph.  You can also select tab-separated file, as well as a few other options.  Further historical data for the Rio Grande can be found at the Rio Grande Historical Mean Daily Discharge Data page.

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.

How many Billion dollar weather/climate disasters occur in the U.S. each year?

NOAA has your answer on their Billion-Dollar Weather and Climate Disasters: Time Series page. The page includes an interactive version of the graph here that allows you to select disaster types and adjust for CPI.  The data is available to download.

Determining the cost of disasters is not simple and they note:

In May 2012, NOAA’s National Centers for Environmental Information — then known as National Climatic Data Center (NCDC) — hosted a workshop including academic, federal, and private sector experts to discuss best practices in evaluating disaster costs.

A research article “U.S. Billion-dollar Weather and Climate Disasters: Data Sources, Trends, Accuracy and Biases” (Smith and Katz, 2013) regarding the loss data we use, our methods and any potential bias was published in 2013. This research article found the net effect of all biases appears to be an underestimation of average loss. In particular, it is shown that the factor approach can result in an underestimation of average loss of roughly 10–15%. This bias was corrected during a reanalysis of the loss data to reflect new loss totals.

A climate.gov post by Deke Arndt (4/13/18) , The all things being equal edition, discusses the connection between weather and climate:

Relative sea level in and around Boston has risen about half a foot in the last 50 years. So, all else being equal, the same storm 50 years ago would have six inches less water to push inland. That’s a big, big difference, and one that has developed on the climate scale.

That’s how climate comes in, even in these weather events. Many times, in the discussion of weather and climate, we mistakenly consider these two words, and the concepts they define, to be mutually exclusive frames.

How much has growing season/allergy season increased in your town?

Climate Central has your answer with their post, Here’s How Frost-Free Season Affects Allergy Season (4/4/18). You will find a drop down menu to produce graphs like this one for Grand Rapids, which has seen as average increase of about 25 frost free days. On the downside,

 A study sampling 10 locations from Texas to Saskatoon, Canada indicated that pollen seasons lengthened between two to four weeks from 1995 to 2009, with the largest increases in the northernmost areas.

In addition, increasing atmospheric carbon dioxide enhances photosynthesis in plants, meaning that they produce more pollen.

They don’t provide the data, unfortunately, but they do provide a clear methodology so that you can create the data set for your city. You can get weather data from NOAA Climate Data Online. There is great potential here for student projects in statistics courses.

How is climate change impacting Easter Island?

A New York Times article,  Easter Island Is Eroding, (3/15/18 by  Casey and Haner) has the answer.

Tourists usually begin their days in Tongariki, where they gather to watch the sunrise from behind a line of monoliths facing inland. Groups split off to Anakena, the island’s one sandy beach, or to the ancient platforms at Akahanga, a sprawling site of former villages on the shore where, tradition holds, the island’s mythical founder, Hotu Matu’a, is buried in a stone grave.

Yet all three sites now stand to be eroded by rising waters, scientists say.

“We don’t want people seeing these places through old photos,” Mr. Rapu said.

A beach is already lost:

The damage has been swift on Ovahe Beach, near where Mr. Huke came across bones in the sun. For generations, there had been a sandy beach here that was popular with tourists and locals. Nearby, a number of unmarked burial sites were covered with stones.

Now the waves have carried off almost all of the sand, leaving jagged volcanic stone. The burial sites have been damaged and it’s not clear how long they will survive the waves.

Walls collapsing:

At a site called Ura Uranga Te Mahina on the island’s southern coast, park officials were alarmed last year when blocks of a stone wall perched about 10 feet above a rocky coast collapsed after being battered by waves.

There is more and the article has fantastic photos.

Where can we find basic climate information?

The answer is Climate Kids by NASA.  Climate kids is aimed at, well, kids, but it serves as a fantastic primer of basic climate science.  For example, under Big Questions and then How do we know the climate is changing? we find short explanations of the following questions (with links to  further resources):  So what if Earth gets a tiny bit warmer? Why is Earth getting warmer? (includes the CO2 graph copied here) How do we know what Earth was like long ago? How can so little warming cause so much melting? Doesn’t rising sea level just bring us closer to the beach? How does climate change affect other species?

The main menu of pages has Big Question. Weather and Climate. Atmosphere. Water. Energy. Plants & Animals. No matter how much you know about climate change, you’ll find something interesting on Climate Kids. You can also do a quick check of what you know with their Climate Trivia game.

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.