Best Effort Global Warming Trajectories

Demonstration using Wolfram CDF Player

Harvey Lam

Princeton University

December 2007 (updated March, 2011)

  In order to deal with the global warming problem, the world's governments need to establish a long term global policy on emission reduction. In short, the world needs to know what to do---i.e. how much needs to be done and by when.

 The usual policy discourse is as follows. A target ceiling for the amount of carbon dioxide in the atmosphere (that can be tolerated by the world) is somehow chosen (e.g. "doubling" of the pre-industrial revolution level is a popular target ceiling), and a strategy---of future carbon dioxide emission reduction---is then sought to achieve this goal. Here, we tackle the problem differently. We specify instead our estimate of the best effort the world is capable of in the future. Our goal is to find the final achievable atmospheric carbon dioxide ceiling when the best effort is made.

 Let E(t) be the carbon dioxide annual emission rate (coming from burning of fossil fuels), C(t) be the total amount of carbon dixoide in the atmosphere (in units of GtC, gigatons of carbon equivalent), and t the time in years offset from the start of the 21st century. Before the industrial revolution, E was essentially negligible, and C was fairly constant at about 600 GtC for several millennia.

At the start of the 21st century, E is approximately 8 GtC/year, C is approximately 800 GtC (divide by 2.12 to get the value in ppmv unit), dC/dt is approximately 4 GtC per year, and dE/dt has been approximately +0.16 GtC/year per year in the second half of the 20th century. About one-third of the carbon emission is for electricity generation, about one-third is for transportation (cars, trucks, airplanes, ships), and about one-third for heating and industrial use.

     The amount of average global temperature rise (above the pre-industrial revolution value) is proportional to ln(C/600)/ln(2), and the proportionality constant is called the carbon dioxide climate sensitivity. The IPCC recommended value for climate sensitivity is approximately 3 degree Celsius (when C is double the pre-industrial revolution value).

  We want to eventually stabilize the value of C(t) in the future at some value higher than the current value. A common target ceiling being discussed in the media is 1200 GtC (or 560 ppmv), the "doubling" of the pre-industrial revolution level scenario. Stabilization of C means the annual carbon emission rate must be substantially reduced.

  Since the current value of dC/dt is positive (about 4 GtC/year), we need to push its value toward zero, and then to maintain it at zero thereafter. To do that, the total task is divided into three periods:

Note that in the first two periods, C(t)---thus the global average temperature---continues to rise with time.

  From the policy point of view, the duration of the transition period is an important parameter. How many transition years should be allotted to the transition period? It takes time for the world to slow down and "stop" the rising world energy demands. The pace of emission reduction in the sustainment period is another important parameter. What is the maximum amount of annual emission reduction can the world achieve when the best possible effort is made? In Pacala-Socolow, a one wedge emission reduction effort was defined as an effort that reduces the global annual carbon emission by one gigaton (GtC) after fifty years. This translates into an average pace of annual emission reductioin of E by -0.02 GtC/year per year. We shall call this level of annual emission reduction effort an one-wedge effort. Thus a three-wedge effort would be to have a emission reduction of -0.06 GtC/year per year during the whole sustainment period. We shall use number of wedges to specify the maximum best effort the world is capable of achieving in the sustainment period (wedge need not be an integer).

  A one wedge effort is roughly the effort of building one Three-Gorges-Dam per year throughout the sustainment period. Pacala-Socolow believe that a seven-wedge effort (starting immediately) is needed to hold E(t) constant in the next fifty years just to meet the expected rising (future) world energy demands. They clearly stated that E(t) must decrease firmly and substantially after these fifty years to honor any reasonable target ceilings.

  A Demonstration using Mathematica’s Wolfram CDF Player has been created as a "what if" tool for policy makers. Click on this:

Best Effort Global Warming Trajectories

 In this demonstration,  the "number of wedges" parameter is the number of wedges needed in the sustainment period IN ADDITION to the whatever effort is needed to meet the rising future energy demand. (The Pacala-Socolow "seven-wedge program" for the next 50 years merely held annual emission constant---to meet rising future world energy demands---and it would be considered a zero-transition/zero-wedge effort for the next 50 years here).

  You do not need to have Mathematica  on your computer to use this tool. If you do not have Mathematica, you need the free Wolfram CDF Player.  If you do not yet have Wolfram CDF Player you need to click on Interact Now! orange box to download it. Follow the instructions to install it, then click on "Download Demonstration" at the upper right corner of the webpage to download the .cdf demo file. Once you have the CDF Player, you can run it and ask it to run the BestEffortGlobalWarmingTrajectories.cdf demonstration file on your own computer. You can play with the two sliders: one for the value of transition years, and one for the number of wedges. The blue curve is the atmospheric carbon dioxide C(t) in GtC (divide it by 2.13 to get the value in ppmv---parts per million). The purpole curve is E(t) x 100 (so that it can share the same ordinate as C(t)). The dashed black curve is the popular 'doubling' target ceiling of 1200 GtC.

  The graph tells us the impact of the two parameters (transition years and number of wedges) on the following questions:

   The media usually talks about the so-called "doubling" target level for C(t) (roughly 1200 GtC or 560 ppmv). This is shown as a black dashed line on the graph. The IPCC estimate of global temperature rise at "doubling" is roughly 3 degrees Celsius. Its dependence on C is logarithmic.

The carbon cycle in this demonstration is based on the one-tank model of Socolow-Lam (with a time-dependent long term sink; see its Appendix B). If you download the "Source Code" and you have Mathematica, you can change all the default parameters in the Socolow-Lam model. Without Mathematica and only the Wolfram CDF Player, you have to stay with all the default parameters.

   Feedbacks are welcome.