METEO 469
From Meteorology to Mitigation: Understanding Global Warming

Problem Set #3

PrintPrint

Estimating Future Warming

Activity

NOTE: 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 I can open it.

For this activity, you will explore the warming due to increases in CO2 using a simple (0d EBM) climate model. You will consider applications to:

  • defining CO2 thresholds for avoiding dangerous human impacts on climate;
  • the controversial notion of 'geo-engineering' as a means of mitigating human-caused climate change.

Online 0d EBM Application

Directions

  1. First, save the  Problem Set #3 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 (e.g., by first printing the output to a pdf file and then directly inserting into the worksheet) to submit along with your discussion and conclusions.
  2. Use the online 0d EBM application to calculate the Earth's mean temperature (pre-industrial, that is, without anthropogenic greenhouse warming) and climate sensitivity (the net warming due to CO2 doubling from pre-industrial) for the (i) low-end, (ii) mid-range, and (iii) high-end IPCC gray body parameter settings. To do that, please use the default settings for the solar constant (S=1370 W m 2 ) and the Earth's albedo ( α=0.32 ), and double the pre-industrial CO2 concentrations. Discuss how the mean temperature and climate sensitivity change depending on the choice of IPCC gray body parameter.
  3. The European Union has defined 2 °C degrees warming relative to the pre-industrial temperatures as the threshold for dangerous anthropogenic interference (DAI) with the climate system. Use the online 0d EBM application to estimate the level of CO2 at which would we expect to breach the DAI amount of warming for the (i) low-end, (ii) mid-range, and (iii) high-end IPCC gray body parameter settings. Once again, use the default settings for the solar constant and the Earth's albedo. NOTE: that the adjustable slider for CO2 only goes up to 560 ppm, so to use higher values you need to enter them by hand into the box below the slider. [See here for a commentary on the notion of DAI by your course author.]
  4. Atmospheric CO2 is currently at about 400 ppm and is increasing by about 2 ppm per year. If we continue to increase CO2 at this rate, how many years will it take until we commit ourselves to DAI, based on the three climate sensitivities (i.e., gray body IPCC parameterizations) considered above? To answer this question, use your results from Question 3. If you were advising policy makers, how many years would you tell them we have to stabilize CO2 emissions and why?
  5. Later in this course, we will encounter the concept of geo-engineering — an approach to climate change mitigation which involves the attempt to offset greenhouse warming through various means of intervention with the climate system. One much-discussed geo-engineering scheme involves shooting sulfate aerosols into the stratosphere, mimicking the natural cooling impact of explosive volcanic eruptions. The eruption of Mount Pinatubo in 1991, for example, caused approximately 2.5 W m-2 reduction in the amount solar radiation incident at the Earth's surface, which is equivalent to about a 14 W m-2 reduction in the solar constant, and the effect lasted over about a 3 year period. (Recall from Lesson 4 that the amount of solar radiation incident at the Earth surface, Fin, relates to the solar constant, S, as F in =( 1α )*S/4 , where α is the Earth's albedo.) Therefore, over a 3 year period, Mt. Pinatubo caused about a 1% reduction in the solar forcing. Use the online 0d EBM application to consider a scenario where we stabilize CO2 concentrations at double their pre-industrial levels. Assuming the mid-range gray body IPCC parameterization, with what frequency would we have to simulate Mt. Pinatubo-like eruptions to keep global mean temperatures from exceeding the 2 °C DAI threshold? HINT: Start by recording temperature (with AGW) for the default values of the solar constant and the Earth's albedo, and double pre-industrial CO2 for the mid-range gray body IPCC parameterization. This setup produces a 3 °C increase in temperature over the pre-industrial CO2 levels. Then, decrease the solar constant until you find that the temperature (with AGW) decreased by 1°C, which results in total 2 °C increase in temperature that we need for DAI (ignore Temperature Change field, as it does not change). Based on the change you applied to the solar constant, approximate the required frequency of Mt. Pinatubo eruptions: one way to think of it is that one Pinatubo every 3 years gives you an average 1% reduction in S, so one Pinatubo every 6 years gives an average 0.5% reduction in S, one Pinatubo every 9 years gives an average 0.33% reduction in S, etc.
  6. An alternative geo-engineering approach involves changing the Earth's surface properties by altering the albedo through various schemes, e.g., painting rooftops white, or artificially seeding low clouds over the ocean. By what percent would we need to increase Earth's albedo to avoid exceeding 2 °C warming relative to the pre-industrial level, under a CO2 doubling scenario and using the mid-range IPCC gray body parameterization? In your opinion, is this is a realistic approach? [HINT: Start by recording temperature (with AGW) for the default values of the solar constant and the Earth's albedo, and double pre-industrial CO2 using the mid-range gray body IPCC parameterization. This setup produces a 3 °C increase in temperature over the pre-industrial CO2 levels. Then, increase the Earth's albedo until you find that the temperature (with AGW) decreased by 1°C (ignore Temperature Change field, as it does not change). Note that the increase will be very small, so it might be easier to enter values by hand into the box below the slider.]
  7. Save your word processing document as either a Microsoft Word or PDF file in the following format:

    PS3_AccessAccountID_LastName.doc (or .pdf).

    For example, student Elvis Aaron Presley's file would be named "PS3_eap1_presley.doc". This naming convention is important, as it will help the instructor match each submission up with the right student!

Submitting your work

  • Upload your file to the "Problem Set #3" assignment in Canvas by the due date indicated in the syllabus.

Grading rubric

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