As we are wrapping up a record setting two week arctic cold spell across the northern regions of the country, I thought it would be nice to think about warmer times to come. The article, It’s Not Your Imagination: Summers are Getting Hotter, also includes some nice histograms if you are covering statistics in your QR class. The histograms clearly show the distribution of summer temperatures for given time periods getting warmer, or moving right on the temperature axis.
I know my students always struggle interpreting histograms so this was a great chance to provide them practice and discuss the record setting year of natural disasters by which 2017 may be best remembered.
The distributions also appear to be spreading out or getting more variable. The authors claim “this effect is mainly a reflection that some parts of the world are warming faster than others. There is no evidence that temperatures are becoming more variable in most parts of the world after warming has been accounted for.” This was challenging for me to wrap my head around and looking up the research paper did little to clarify. There was this line from the paper that seemed helpful: “In terms of relative magnitude, an increase in variance for regions of low standard deviation will outweigh a similar decrease for a region of high variation.” This sounds a little like the classic problem of increasing $100 by $20 is a 20% increase, but decreasing $200 by $20 is only a 10% decrease.
I did include some the graphics from the research paper in my weekly take-home quiz, but wasn’t able to offer a fully convincing rationale for this argument. Please post comments if you have a good way of explaining why we can conclude there is no evidence of temperatures becoming more variable after warming has been accounted for. In any case, it was a perfect topic for our discussions of distributions of data, and z-scores!
- The article, It’s Not Your Imagination: Summers Are Getting Hotter, has lots of histograms.
- These bell curves (shown above) are actually histograms. So for a given period (say 1951 – 1980) and a given location in Northern Hemisphere (where most of the land mass is) they measure the average temperature for every day in the summer. They then put all the data together (from every location). What would a bin (crate) represent in the histogram?
- What would the height of a column in the histogram represent?
- Which data set, 1951-80 or 2005-15, has a larger standard deviation? Explain!
- The following quote is confusing: “ Hansen’s curves also flatten out, which some have suggested is an indication of greater temperature variability. But other climate scientists …have pointed out that this effect is mainly a reflection that some parts of the world are warming faster than others.”
So the distribution of average daily temperatures (at a given location) has a mean and standard deviation over a period of time. They then convert the average daily temperatures to z-scores by subtracting the mean from each daily value and dividing by the standard deviation. The distributions in Figure a are showing z-scores for different periods by always subtracting the mean from 1958-1970. If instead you subtract means for each period you get these distributions in Figure b and the shift disappears. Mathemagic!
Further math shenanigans yields Figure g showing the global standard deviation getting smaller over time:
In DLS Joel Best discusses organizational practices and how choices must be made that affect the statistics computed. Discuss how organizational practices impact whether we conclude temperatures are getting more or less variable.
- Joel Best discusses how big numbers confuse people.
- Compute how long 1 thousand seconds is in minutes.
- Compute how long 1 million seconds is in days.
- Compute how long 1 billion seconds is in years.
- Compute how long 1 trillion seconds is in years.
- Complete the following analogy: A penny is to $10,000 as _________ is to $1 trillion. The value you just put in the blank is like a penny to the U.S. government’s budget.