1. To understand that human perception of climate change depends on the magnitude of change of a climate variable (such as temperature) in comparison to its natural variability.

2. To develop familiarity with the content of the ESRL/GMD climate database.

3. To develop skill in accessing, manipulating, and interpreting those data.

4. To understand that climate science has a fundamental statistical quality.

This module is intended as a combination of in-class discussion, in-class group work, and out-of-class exploration, at the undergraduate level. I recently taught this module as part of 400-level capstone core course titled Science and Economics of Climate Change. The course had no prerequisites other than a set of core disciplinary areas, including a semester of science and a semester of math, but no particular science or math course. The audience, therefore, were juniors and seniors, mainly Economics, Biology, and Chemistry majors. The exercise could also work in other courses exploring the measurement of climate change.

Prior to the exercise, the class discussed differences between weather and climate -- especially, the fact that climate science is a largely statistical science, in which a period of thirty years is the conventional minimum necessary to establish what a climatological mean. We also discussed the quantitative meaning of standard deviation, e.g., as a measure of the width of a distribution.

Complementing the computational work, students were tasked with reading and discussing a 2016 paper by Hansen and Sato, Regional Climate Change and National Responsibilities (see link in References and Resources). In this well-cited paper, the authors carry out a similar statistical analysis of regional trends in temperature to what students carry out. Hansen and Sato assert that human perception of climate change depends on the shift in a climate variable (say, of temperature) relative to its natural variability. They go on to show that some regions of the planet have experienced greater shifts in temperature compared to the variability. Hansen and Sato also discuss regional distributions of historical responsibility for climate change, as well as current emissions of greenhouse gases.

In Science and Economics of Climate Change, the activity was sequenced in the following way:

1. (15 minutes) In class, I give a lecture describing the goals and methods of the exercise, including a brief introduction to the Hansen/Sato paper. Here is a powerpoint with figures extracted from that paper: Slides for figures from Hansen/Sato 2016 paper.

2. (15 minutes) Also in class, I lead a hands-on coaching session in which students get out laptops and I verify that each group of students is able to launch a spreadsheet program, and access the ESRL/GMD database. I also provide a brief exposition of essential statistical ideas, especially the mean and standard deviation of a distribution.

3. (1-2 hours) Out of class, students watch supplementary videos, do the assignment, upload their results for evaluation, and read assigned sections of the paper by Hansen and Sato.

4. (20 minutes) In a subsequent class session, I lead a discussion on student results and the Hansen/Sato paper.

It will help if students already have some familiarity with basic spreadsheet program functions. Prior understanding of how to construct a histogram is not necessary, however, as it is a learning objective of the exercise. A class of 15-20 students is manageable by a single instructor, provided students work in groups of two or three, and these groups are able to help one another. Larger classes can be accommodated with instructor assistants.

The Hansen/Sato paper is probably too challenging for undergraduates to fully understand within the time framework imagined here. But it is not necessary for students to understand it in full: they can consult specific figures and paragraphs, as assigned. The module could also be taught in a high school setting, although with perhaps more time allocated for each step.

Students, in groups, were tasked with choosing a location, with the help of a visual representation of the globe (in our case, this was done in software, but any representation would do). Before proceeding, the entire class was surveyed to ensure a reasonably global coverage. Groups were then tasked with downloading surface temperature data from the closest available NOAA Climate Monitoring Division's data archive. Two datasets from the same month (at a selected location) were downloaded, one recent and another from decades earlier. Students then investigated statistics of these temperature records by constructing temperature histograms (probability distributions as a function of temperature).

Materials included access to the internet and a laptop computer with a spreadsheet program. The 2016 paper by Hansen and Sato referred to above is freely available online (see link in References and Resources).

Some coaching may be necessary on how to navigate the ESRL/GMD website, and on how to construct a histogram in a spreadsheet. I do much of this coaching via videos made available to students outside of regular class time. Sample videos supplied with this submission (see links in References and Resources).

In reference to the assessment items, here are some tips:

• Climate science can be thought of as a study of the statistics of weather. For that reason, climate scientists emphasize visualizations like histograms of variables.
• The critical threshold of shift-to-variability is an advanced statistical topic; here the emphasis is on qualitative judgement.
• The Hansen/Sato paper contains data similar to the kind of histograms students produce in this exercise, but over a global geographical extent. Also, the authors have re-scaled the horizontal axis in terms of standard deviations of temperature.
• The Hansen/Sato discussion of national responsibilities (in addition to perceptions) may be interesting for students to explore and discuss, but it is not essential to understand in order to complete the assigned task of constructing a histogram.
• At the heart of the discussion of conventions that govern the content of figure captions vs narrative, is a more important distinction between objective and subjective interpretations of data.

One fundamental message, almost unavoidably taken home, is that measuring the impact of climate change as an average masks the vital fact that projected regional impacts of climate change vary considerably: some regions will experience change far in excess of the average. Moreover, the degree of exposure to climate change is not correlated with either the historical responsibility, nor current emissions of greenhouse gases. It is difficult for students, after this exercise, to consider climate change as anything but a global phenomenon that requires long-term measurements to comprehend.

Students submit their temperature histograms, with captions and a brief narrative. Here is a sample submission, Temperature histograms from Barrow, and a grading rubric, Grading rubric for histogram submission.

During the instructor-mediated conversation, students compare their results to those reported by Hansen and Sato, 2016. Questions you may wish to raise in this context include:

• Climate scientists and meteorologists deal with similar variables (e.g., temperature and precipitation), but differ greatly in how they work with those variables. What differences can you identify?
• A decadal shift in the mean temperature of a given region is perceivable if that shift is significant compared to the natural variability in temperature. In students' opinion, what is the critical threshold of shift-to-variability ratio, to influence popular perception of climate change?
• Based on data provided by the class, and/or presented in Hansen and Sato, in what regions of the planet is human perception of climate change to be more or less likely?
• Hansen and Sato show that the regional distribution of perceptions of climate change differs from the regional distribution of historical responsibility for climate change. Why do they consider this an important finding?
• There are conventions that govern the information content appearing in the caption of a figure vs in the part of the narrative that discusses the figure. Based on your reading of the Hansen/Sato paper, what do these conventions appear to be?

2016 Paper by Hansen and Sato: http://iopscience.iop.org/1748-9326/11/3/034009

NOAA's ESRL/GMD link: https://www.esrl.noaa.gov/gmd/dv/ftpdata.html

Video on how to import data from NOAA's ESRL/GMD website: https://youtu.be/Ah4wFu5sv0c

Video on how to make a histogram in Excel: https://youtu.be/MwgQojNasPw