Climate and Climate-System Modelling - Environmental Modelling: Finding Simplicity in Complexity - page 155

coal that are used along with their CO 2 emission factors
are used to compute the global fossil fuel CO 2 emissions.
Worksheet 11 contains an interface for optionally using
CO 2 emissions from the more detailed calculations in
the online material associated with Harvey (2010a, b), in
place of the emissions fromWorksheet 10.
The absorption of CO 2 by the oceans involves a
sequence of processes occurring at successively slower
rates: initial rapid (within one year) air-to-sea trans-
fer of gaseous CO 2 , then gradual mixing of dissolved
inorganic carbon progressively deeper into the ocean. A
pulse of CO 2 that is injected into the atmosphere can be
divided into a series of fractions, each of which decays
(decreases in concentration) with its own time constant.
This mathematical representation is referred to as the
impulse response for CO 2 .
A continuous emission of CO 2 can be represented by
a series of annual emission pulses, each of which decays
according to the impulse response. The amount of CO 2
in the atmosphere at any given time is the sum of the
amounts remaining from each of the preceding annual
pulses going back to the beginning of human emissions.
Due to the nonlinear carbon chemistry of ocean water,
the rate of decay of successive pulses becomes slower as
the cumulative emission (and hence, absorption by the
oceans) increases. This slowing can be represented by
adjusting the coefficients in the impulse response as a
function of the cumulative emission. Worksheet 12 con-
tains the impulse responses that are to be used in succes-
sive time intervals as the cumulative emission increases.
Worksheets 13 to 17 carry out the calculation of the
increase in atmospheric CO 2 concentration, total radia-
tive forcing and the change in global mean temperature.
The total CO 2 emission is summed up in Worksheet 13
and used with the impulse functions from Worksheet 12
to compute the increase in atmospheric CO 2 concen-
tration. The total emission involves fossil-fuel emissions
(from Worksheets 10 or 11), emissions due to land-use
changes (such as deforestation) and the production of
cement, emissions from the terrestrial biosphere other
than through land-use changes (where absorption of
CO 2 is a negative emission), direct emissions of CO 2
from thawing permafrost soils, and emissions CO 2 from
the oxidation of methane from fossil fuel sources (such as
leaks in natural gas distribution systems) or from thaw-
ing permafrost soils. Emissions from land-use changes
and the production of cement are derived from parame-
ters that are specified in the worksheet. The CO 2 emission
fromoxidation of fossil fuel methane depends on the user-
specified fossil fuel methane emissions and the methane

lifespan in the atmosphere, which depends in part on the
methane concentration itself. Net CO 2 emissions from
the terrestrial biosphere depend on the CO 2 concentra-
tion (through the stimulation of photosynthesis by higher
CO 2 ) and on change in temperature (which affects both
photosynthesis and respiration), but the CO 2 concen-
tration and temperature change depend in part on the
emissions, so there is a climate-carbon cycle feedback
loop. Another feedback loop exists through the depen-
dence of CO 2 and CH 4 emissions from yedoma soils
(Crich soils in Siberia) on the temperature change. Emis-
sions from (or absorption by) the terrestrial biosphere are
computed in Worksheet 14 (which uses a four-box ter-
restrial biosphere model rather than a three-box model),
while emissions of CO 2 and CH 4 from thawing yedoma
soils are computed in Worksheet 15. Worksheet 13 also
contains calculations for the buildup of atmospheric
methane and nitrous oxide (N 2 O) concentrations and for
emissions by sulphur aerosols, all based on a handful of
parameters that can be altered by the user and which are
fully explained in the online supporting information.
Worksheet 16 contains the calculation of the radiative
forcing (heat trapping or, in the case of aerosols, reflection
of solar radiation) due to the buildup of CO 2 ,CH 4 and
N 2 O, as well as due to tropospheric ozone, stratospheric
water vapour, and aerosols. Also included up to 2000 are
estimated radiative forcings due to changes in the solar
luminosity and due to volcanic eruptions. Worksheet 17
uses the total radiative forcing to compute the change
in surface temperature using the two box model that is
featured in Worksheet 6.

9.4.4 Conservationof energyandmass
The final worksheet presents a series of model diagnostics
that illustrate conservation of mass and conservation of
energy. Research by Sterman and Sweeney (2007) indi-
cates that the public's concepts of the relationshipbetween
changes in emissions and changes in CO 2 concentration,
and between changes in CO 2 concentration and changes
in temperature violate the principles of conservation of
mass and energy. This perception arises because people
tend to assume that changes in concentration immediately
track changes in emissions (rather than depending on the
difference between sources and sinks) and the changes in
temperature in turn immediately track changes in CO 2
concentration (rather than depending on the current
radiation balance). This tendency was found to be true
of graduate MBA and engineering students at Harvard
even after first explaining the difference between stocks