Global CO2 Concentration Modeling
Beth Kephart
An energy scenario constructed by the World Energy
Council shows that by the year 2100 our energy demands may
be four times greater than at the present moment. If CO2
concentration in the atmosphere followed the same trend, the
results could be a problem. Under certain conditions the CO2
concentration can head towards a future steady-state value,
even for increasing global energy use; however, future fossil
fuel use would have to decrease to a fraction of what it is now,
and the factor of carbon lifetimes leads to process time delay.
For this particular model, results are based on the conditions
which lead to only a doubling of CO2 concentrations by the year
2100, or a value of 550 ppmv.
Classical carbon cycle models have been used in the
past to predict future atmospheric CO2 concentrations.
The errors in these models are quite large because there is
a lack of precise knowledge about the carbon budget itself.
For the model focused on here, the CO2 concentration change
is considered with parameters of the key determinants found
by combining econometric regression (mathematical analysis
methods applied to economic research) with a recent dataset.
It was determined that the annual changes in atmospheric CO2
concentration should be described by (1) a variable for
concurrent anthropogenic carbon emissions and (2) a variable
for lagged stock or "seepage", representing the equilibration
process between the deep ocean and surface waters, as well as
reactions in ocean chemistry (CO2 content and ocean temps.
The econometric equation originates from the Nordhaus
and Yohe (1983) specification, modified by Cohen and Collette
(1991):
Change(AC(t)) = k + m1m2*E(t) - m3AC(t-1) +
e(t)
where:
Change(AC(t)) = annual change in the atmospheric conc.
of CO2 (in ppmv)
k = intercept, allows for equilibrium in the natural
carbon cycle (i.e. in the absence of emissions)
m1 = conversion factor (=0.471, emissions in GtC to ppmv)
m2 = marginal airborne coefficient
E(t) = anthropogenic carbon emissions
m3 = coefficient of seepage into carbon sinks
AC(t-1) = lagged atmospheric stock of CO2 (1 year lag)
e(t) = error term
Also, the value of the regression intercept k should satisfy
the following two conditions: (1) the initial year conc. change
of the fitted regressions should be close to the conc. change
from the Sipole ice-core data in the middle of the 19th-century,
where in this period there were no anthropogenic emissions, and
(2) the fitted regressions should result in a natural equilibrium
of CO2 concentrations that is realistic (equilibrium is set
when Change(AC(t)),E(t)=0 and k=m3AC(t-1)).
The dataset spans the time period 1860-1986, and includes
values for global fossil-fuel emissions, emissions from land
use including deforestation, and global CO2 concentrations.
When parameters were found, a final solution was yielded by Cohen
and Labys (1994):
Change(AC(t)) = .277 + .225*E(t) - .00116AC(t-1) + e(t)
The equation solution shows a time path leading to a steady-state
CO2 concentration of 550 ppmv by the year 2100. The time paths of
future CO2 concentration and emissions variables is as follows:
Presently (1995):
AC(t) = 362.1 ppmv
Land-use change emissions = 1.4 GtC
Industrial emissions = 6.4 GtC
Total emissions = 7.8 GtC
For the years 1995 to 2100:
AC(t): rising to a cap of 550 ppmv in 2100
Change(AC(t)): decreasing rates of change over time
Land-use change emissions: rise until 2035 (2.1) then
fall to a value of zero in 2100
Industrial/total emissions: rise until 2050 then fall
to a value of 1.4 GtC in 2100, where all
emissions are seen as industrial (land use = 0)
For the years 2100 and beyond:
AC(t): steady-state at 550 ppmv
Land-use change emissions : zero
Total emissions=industrial: steady-state at 1.6 GtC
In order for this model to work, the decline of industrial
carbon emissions must come from cutting back on fossil fuel
use. This may or may not be a practical model for the future
since we do not know what our future energy options are yet.
However, it is important that we look into non-carbon energy
sources today to plan for the effects of carbon emissions in
the future.
Reference
Cohen, Bruce C. and Walter C. Labys, 1996: Uncertainty, carbon dioxide concentrations and fossil fuel use.
International Journal of Environment and Pollution, 6.
