Structure and Composition of the Present-Day Atmosphere - Air Pollution and Global Warming: History, Science, and Solutions - page 60

The seasonal fluctuation in CO 2 (g) is due to the sea-
sonal cycle of photosynthesis and bacterial decompo-
sition of annual plants (plants that germinate, flower,
and die during a year), deciduous trees (trees that lose
their leaves seasonally), and coniferous trees (trees
with cones, needles, or scalelike leaves that lose their
needles annually but are mostly evergreen). Such veg-
etation generally grows at high latitudes, outside the
tropics. When annual plants, deciduous trees, and conif-
erous trees grow during the spring and summer, photo-
synthesis removes CO 2 (g) from the air, increasing plant
mass. When such plants die during the autumn and win-
ter, their decomposition by bacteria adds CO 2 (g) to the
air, reducing plant mass. Because the Northern Hemi-
sphere contains much more land area and plant mass
than does the Southern Hemisphere, CO 2 (g) reductions
are dominated by photosynthesis during the Northern
Hemisphere spring and summer. In fact, the seasonal
reductions in Figure 3.11 always start in May and end
in October. Because tropical plants are mostly ever-
green (maintaining their leaves during all seasons), they
contribute less to the seasonal CO 2 (g) cycle than does
vegetation at higher latitudes.
Typical indoor mixing ratios of CO 2 (g) are 700 to
2,000 ppmv but can exceed 3,000 ppmv when unvented
appliances are used (Arashidani et al., 1996).

a ,so a must be calculated in a time-dependent

manner.
The rate of change of the anthropogenic mixing ratio

( a , ppmv) of CO 2 (g) or any other gas with a con-

stant emission source ( E , ppmv yr − 1 ) and a specified
e -folding lifetime ( , years) against overall removal

from the air can be calculated over time ( t , years) by
solving

d a ( t )

dt

− a ( t ) = E (3.20)

where a ( t )isthe anthropogenic mixing ratio expressed

as a function of time. To determine the CO 2 (g) lifetime
used in this equation, which varies in time slowly, it is
necessary first to rearrange the equation as

a ( t )

= (3.21)

E − d a ( t ) / dt

The lifetime can be determined from data by using
the CO 2 (g) mixing ratio a ( t ) and its slope over time

from Figure 3.11 (assuming 275 ppmv) and an

annually varying anthropogenic emission rate consist-
ing of a fossil fuel emission rate from Figure 12.11,
plus a permanent deforestation emission rate of 1,500 to
2,700 Tg-C yr − 1 .Because the lifetime determined from
Equation 3.21 is constrained by data, it is referred to
as the data-constrained e- folding lifetime of CO 2 (g) .
The data-constrained lifetime represents the overall life-
time against CO 2 (g) loss by all processes in Table 3.6.
Whereas each individual loss process, acting on its own,
would cause CO 2 (g) to have a different lifetime, the
overall lifetime accounts for the aggregate of individual
process lifetimes in a manner similar to Equation 1.13.
However, unlike Equation 1.13, the data-constrained
lifetime is obtained directly from observations rather
than estimates. The data-constrained lifetime varies
over time, accounting for the fact that as conditions
change on the Earth, the lifetime changes as well.
Figure 3.12 shows the data-constrained e -folding life-
time of CO 2 (g) since 1960 calculated in this man-
ner. The figure indicates that the lifetime has slowly
increased but has historically ranged from around 30 to
50 years, with a rough mean of

b =

3.6.2.3. Equation for Estimating Mixing Ratio
Formany types of analyses, it is useful to estimate
the past, current, or future globally averaged mixing
ratio of CO 2 (g). Here, a simple yet relatively accurate
equation is presented that depends only on the emission
rate, overall lifetime against removal, and preindustrial
mixing ratio of CO 2 (g).
The mixing ratio ( , ppmv) of CO 2 (g) can be

expressed as b is the back-

ground or preindustrial mixing ratio prior to 1750
and

= b + a ,where

a is the anthropogenic mixing ratio ,which
is the mixing ratio due to anthropogenic emissions
since 1750. The year 1750 precedes the Industrial
Revolution (Section 4.1.3). Because the preindus-

b =

trial mixing ratio was relatively constant ( 275

ppmv) averaged over hundreds of years before 1750,
preindustrial emission rates of CO 2 (g) are in rela-
tive equilibrium with preindustrial mixing ratios, so
a time-dependent expression for

40 years. The
increase in lifetime with time is due in part to the
fact that CO 2 (g) solubility in ocean water decreases
with increasing temperature. Because ocean tempera-
tures have been increasing, the relative rate of atmo-
spheric CO 2 (g) dissolution into ocean water has been

∼

b is not needed
for analyses on time scales of several hundred years.
However, because anthropogenic emissions have been
increasing over time, they are not in equilibrium with