Quantum mechanics: Polar spectra

Penny Rowe, NorthWest Research Associates; Steven Neshyba, University of Puget Sound; and Aedin Wright, University of Puget Sound

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Initial Publication Date: March 9, 2020 | Reviewed: March 12, 2023


Students learn about the greenhouse effect by examining a "forbidden" rovibrational band in the infrared emission spectra of Earth's atmosphere, recorded from the surface at South Pole Station. By weighting rotational energy degeneracies with a Boltzmann factor, they simulate the R-branch of the band; the result is a rudimentary estimate of the average temperature of the troposphere above the South Pole. A second activity simulates radiative emission in a saturated part of the spectrum as a Planck Blackbody, which yields the temperature of the atmosphere just above the surface. All computations and graphical displays are done in Jupyter Notebooks.

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Learning Goals

Students download and analyze spectra of downwelling infrared radiance from polar regions and investigated spectra structure due to rovibrational transitions. This analysis is scaffolded by a Computational Guided Inquiry (CGI) module composed of three Jupyter Notebooks, which they use to conduct inquiry in the role of a scientist through making calculations and producing and examining plots. Critical thinking and active inquiry is promoted by open-ended responses to prompts (Pause for Analysis questions). Specific learning goals are as follows:

  1. Learn about the greenhouse effect.
  2. Learn how to download and plot a downwelling radiance spectrum from polar regions.
  3. Understand how gases contribute to the greenhouse effect, which are the most important, and how these contributions are unique in Polar Regions.
  4. Examine infrared spectral features due to rovibrational transitions.
  5. Learn how to model the populations of rotational states according to degeneracy and temperature.
  6. Learn how to use that population to infer an effective temperature of atmospheric CO2 in a downwelling emission spectrum from South Pole Station, Antarctica.
  7. Learn how blackbody radiation is related to downwelling radiation from the atmosphere.
  8. Learn how to use the Planck function and a downwelling radiance spectrum to estimate the surface temperature.

Context for Use

This activity is designed to be used in an upper-level Quantum Mechanics, Quantum Chemistry, or Physical Chemistry course. It has also been adapted for a lower-level Engineering Physics course. Students must have in-class access to computers with internet access and with Jupyter Notebook installed. A computer lab with pre-loaded software can be used or, as in successful pilots, students can download the software onto personal laptops before class (instructions are provided). Problems can be mitigated by having students work in pairs and having an extra laptop or two available as needed, equipped with the software. The activity has successfully been taught in over several class sections or in a longer lab section, for classes of 11 students or less, and is appropriate for up to 30 students. Application in large classes can be fostered by additional support, if available; e.g. through teaching assistants. The activity typically takes 3 to 5 hours and includes homework assignments. No previous computational or coding experience is required. The instructor will give an introductory lecture on the quantum-mechanical concepts, assign pre-module homework, guide the students in working through the module, and facilitate group discussions. The module is adaptable – either of three parts can be used or modified, as has been done for a lower-level Engineering Physics course.

Description and Teaching Materials


In this module, students will work actively with polar data through computer programming in Jupyter with Python. The instructions and notebook are designed so that no prior coding experience is necessary on the part of the student or instructor. This module includes three Jupyter Notebooks, which can be taught sequentially or divided between class periods. Preparation for each can take place at once before all are completed, or before each. All materials needed to implement the activity are provided below. Links to online resources used are provided and digital backups are included in case data is moved or removed. The following describes activities and the materials used for each.

What do the student modules look like? Take a quick look at how the Rovibrational_spectra_1, Rovibrational_spectra_2, and Rovibrational_spectra_3 modules look in Jupyter Notebook. (These are static images. For the interactive versions, see the instructions and materials below).


  • Student setup guides (Zip Archive 1.2MB Apr29 20). After unzipping, this includes:
    • finding_moving_files_mac.docx, finding_moving_files_pc.docx: File management on your computer
    • installing_running_jupyter_mac.docx, installing_running_jupyter_pc.docx
    • Introduction_to_python3.ipynb: Python3 tutorial, to be run in Jupyter Notebook
  • Student materials (polar_spectra.zip) (Zip Archive 3.6MB Jun26 20). After unzipping, this includes:
    • Rovibrational_spectra_1_Introduction_to_polar_data.ipynb
    • Rovibrational_spectra_2_Remote_temperature_sensing.ipynb
    • Rovibrational_spectra_3_Blackbody_radiation.ipynb
    • Ancillary files that need to be in the same folder with the notebook key: band_001_100.txt, ch4.txt, co2.txt, h2o_self.txt, h2o.txt, nu.txt, T.txt, other.txt, humidRS80.py, plancknu.py, radtran.py, IRspec_noaa.png, radiative_balance.png, sgp_aeri_20170706.000443.txt.
  • . After unzipping, this includes:
    • Rovibrational_spectra_1_key.ipynb
    • Rovibrational_spectra_2_key.ipynb
    • Rovibrational_spectra_3_key.ipynb
    • Ancillary files that need to be in the same folder with the notebook key: band_001_100.txt, ch4.txt, co2.txt, h2o_self.txt, h2o.txt, nu.txt, T.txt, other.txt, humidRS80.py, plancknu.py, radtran.py, IRspec_noaa.png, radiative_balance.png, sgp_aeri_20170706.000443.txt (these are identical to those above but are duplicated here for convenience).
    • Rovibrational_spectra_rubric.docx: Answers to questions and rubric.
    • Digital data backup: smtaerich1nf1turnX1.c1.20101228.000313.cdf, which needs to be in the same folder with the keys.
  • Digital Backup: CO2 concentration (as of 2020 March) (Acrobat (PDF) 238kB Mar8 20)

Instructor Preparation

  1. Download materials above and unzip files.
  2. Follow the workflow below.
  3. Compare the completed notebooks to the provided keys and review the answers to questions and rubric in the Assessment materials.
  4. Modify the notebooks as desired and/or include only a portion of them.
  5. You may optionally choose to use the Climate Change videos in References and Resources.


  1. The instructor provides the setup guides to the students.
  2. Students work through the setup guides. They follow the instructions for installing Jupyter on a Mac or PC and work through Introduction_to_python3.ipynb in Jupyter. (Alternatively, the instructor ensures the software is available in a computer lab that will be used.) Students then follow instructions for finding and moving files on a Mac or PC. These tasks have been found to bog down class time for students who are not experienced in them, so we suggest assigning them as homework and reserving some class time afterward to follow up as needed.
  3. The instructor gives an introductory lecture, e.g. explaining that the class will now apply concepts of Quantum Mechanics to a real-world example: rovibrational transitions and blackbody radiance in spectra of the polar atmosphere. The instructor introduces the relevant material, provided in the introduction to the first notebook.
  4. The instructor may optionally have students watch climate change videos to help transition students to the topic (see references and resources below).
  5. The instructor provides the Polar Spectra module files to students. Students put all the files together in a folder on their computer. (Note that *.ipynb files cannot be opened with the text editor; they must be saved to the computer and opened from Jupyter Notebook). Instructors typically make the files within available for the students on Google Drive or a platform used by their institution, and direct students to put the files into a directory on their computers.
  6. Working at a computer singly or in pairs, students complete the modules. The instructor walks around the class, helping as needed. The instructor may choose to iterate through steps 1-6 for each Jupyter Notebook, or do the Jupyter Notebooks as a block.
  7. After students wrap up, the class meets as a group to discuss student responses to the Pause for Analysis questions as well as any observations or questions.
  8. The instructor wraps up the activity by linking the student work back to the original goals.

Teaching Notes and Tips

Digital Backups

  • As they work through the module, students will be prompted to download a polar spectrum. Because data archived online is sometimes moved or removed, a backup version of the file students will need is provided in the Assessment zip file: smtaerich1nf1turnX1.c1.20101228.000313.cdf. (Please note that this is not a Mathematica file, but rather is a netcdf file, which will be loaded in from within the Jupyter Notebook module). We suggest having this file available to share with students (e.g. on a thumb drive) in case it is needed.
  • In addition, the CO2 concentration (as of 2020 March) is provided as a digital backup.

Computer lab vs personal laptops

While students can use a computer lab or work on individual laptops, we suggest the latter. Installing Jupyter Notebooks on laptops is straightforward, gives the students a valuable experience, and allows them to complete work at home, if needed. Furthermore, the student has the computational tool available to them after completion of the activity.


Successful completion of the CGI module is expected to be indicative of meeting the learning objectives. Assessment includes in-class assessment of the module as students work as well as grading of completed notebooks and Pause for Analysis responses. A rubric is provided. Files in the Assessment zipped file include the keys to the notebooks and ancillary files needed to run them, as well as a document containing a suggested rubric and answers to questions. Although suggested scores are given for all questions, the instructor may choose to grade only selected questions.

References and Resources

Climate change videos:


  • Jupyter Notebook
  • Python version 3
  • References and resources contained within the Jupyter Notebook, permafrost.ipynb, include figures from the literature as well as use of web sites and are attributed within the notebook.