From Meteorology to Mitigation: Understanding Global Warming

Problem Set #4


Modeling the Earth's Climate Using One-Layer Energy Balance Model



For this assignment, you will need to record your work on a word processing document. Your work must be submitted in Word (.doc or .docx) or PDF (.pdf) format so the instructor can open it.

For this activity, you will explore the warming of the surface and the atmosphere due to increases in CO 2 using a one-layer EBM climate model. You will consider/investigate the role of various feedbacks in the climate system (water vapor, ice, and clouds), the influence they have on climate sensitivity, and the impact of the uncertainties in the precise magnitudes of the feedbacks.

Link to The One Layer EBM Application


  1. First, save the Problem Set #4 Worksheet to your computer. You will use this word processing document to electronically record your work in the remaining steps.
    • Save the worksheet to your computer by right-clicking on the link above and selecting "Save link as..."
    • The worksheet is in Microsoft Word format. You can use either Word or Google Docs (free) to work on this assignment. You will submit your worksheet at the end of the activity, so it must be in Word (.doc or .docx) or PDF (.pdf) format so the instructor can open it.
    • Please show your work!  When you are explicitly asked to create plots in a question, please cut-and-paste graphics and the output from the screen to submit along with your discussion and conclusions.
  2. Using the online one layer EBM application, double the CO 2 concentrations relative to the pre-industrial level and calculate the climate sensitivity and warming of the mid-troposphere for the following three cases: (A) no feedbacks (i.e., cloud feedback, water vapor feedback, and ice feedback factors all set to zero); (B) mid-range feedback factors (i.e., the default settings of -0.83 for cloud feedback, 2 for water vapor feedback, and 0.5 for ice feedback); (C) high-end estimates of the feedback factors (i.e., the highest settings allowed by the sliders). How does your calculated climate sensitivity range compare with the prevailing range of climate sensitivity estimates? In each case, does the mid-troposphere warm more, the same, or less than the surface? Is this pattern of warming consistent with the predictions by the state-of-the-art climate models? If not, what physics do you think might be missing in our one-layer model?
  3. For the doubling of CO 2 for the same three cases (A), (B), and (C) explored in Question 2, please answer the following questions. What are the long wave and short wave forcing, and the total surface forcing (i.e., the sum of the two)? Calculate the overall feedback factor. To do that, first take the ratio of the total surface forcing to the forcing due to the direct radiative impact of CO 2 doubling alone, which simply equals the total forcing in the "no-feedback" case (A); then subtract one from this ratio. What are the Earth's albedo and the atmospheric emissivity? For cases (B) and (C) is there a change in the Earth's albedo and atmospheric emissivity compared to the "no feedback" case (A)? Which feedbacks could be responsible for the observed changes in each case?
  4. Save your word processing document as either a Microsoft Word or PDF file and submit to the appropriate location in Canvas.

Submitting your work

  • Upload your file to the "Problem Set #4" assignment in Canvas by the due date indicated on our Canvas calendar.

Grading rubric

The instructor will use the general grading rubric for problem sets to grade this activity.