**Best Effort Global Warming Trajectories**

*Demonstration
using Wolfram CDF Player*

lam@princeton.edu

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.

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:

- (i) A
when E(t) is made to peak---E(t) stops rising and begins falling.*transition period* - (ii) A
when E(t) decreases steadily.*sustainment period* - (iii) A
when E(t) merely needs to make minor adjustments to hold C(t) approximately constant.*maintenance period*

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

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 MathematicaÕs 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:

- what is the eventual atmospheric carbon
dioxide ceiling when the
world's atmospheric CO2 is stabilized,
- how long is the sustainment period and how it depends on the number of
wedges,
- what is the eventual amount of annual
emission allowed in the maintanence period and what is the magnitude of the total job.

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.