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OCR for page 62
7
MATHEMATICAL MODELING OF GREENHOUSE WARMING:
HOW MUCH DO WE KNOW?
J. D. Mahlman
For many decades scientists have known that a buildup of carbon
dioxide (002) in the atmosphere has the potential for warming earth's
climate through the so-called '"greenhouse" effect. Over the past 10
years, awareness has grown that other greenhouse gases can contribute in
total to climate warming at a level comparable to that of CO2. These
include human-produced chlorofluorocarbons (CF2C12, CFC13, and others),
methane (CH4), and nitrous oxide (N2O). The atmospheric concentrations
of these gases are currently increasing at a rate sufficient to produce
substantial atmospheric consequences over the next century.
These other greenhouse gases are well known to contribute to very
significant expected changes in the atmospheric ozone structure and
amount. Their potential to add to the CO2 climate warming effect is not
as universally appreciated. Here, I will emphasize only the expected
climatic effects of the ensemble of greenhouse gases.
The information that I will present is derived from three-dimensional
mathematical models of the climate system. A simplified schematic of the
various relevant physical processes is given in Figure 7.1. Such com-
prehensive global climate models have been under intense development at
the National Oceanic and Atmospheric Administration's (NOAA) Geophysical
Fluid Dynamics Laboratory (GEDL) for over 25 years. Climate models have
grown slowly but steadily in scope, complexity, and computational reso-
lution over that period. Accompanying this growth is an improvement in
the ability of the models to simulate the current climate. Accordingly,
modeling atmospheric responses to changing conditions (e.g., seasonal and
daily cycles, different planets (Mars and Venus), and ice age conditions)
has become progressively more accurate.
Unfortunately, substantial uncertainties remain due to deficiencies
in scientific understanding and insufficient computer power. However,
significant progress is expected on both fronts over the next 10 years.
Computer power is increasing while its relative cost is still decreasing.
The impact of model dependence on computer power may be seen in Figure
7.2. Deficiencies in scientific understanding of such areas as ocean
circulation, cloud processes, land surface processes, and chemical
interaction will continue to yield gradually to intense scientific
inquiry. In addition to the models, adequate data are necessary to
evaluate results of the model calculations.
62
OCR for page 63
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ADVECTION
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TRANSFER 1 - - - OF WATER VAPOR
~ l
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HEAT BALANCE HYDROLOGY
OF THE EARTH'S SURFACE
FIGURE 7.1 Simplified schematic diagram illustrating some of the in-
teractive atmospheric processes governing earth's climate system. A
proper climate model must account for all of these processes (and more)
consistent with the laws of physics at a large number of points on the
model "earth."
Current Climate Model Resolution (No Ocean)
5° latitude (300 n miles) X 5° longitude X 10 levels
(36 X 72 X 10 = 25,920 grid points)
Improved Resolution
2.5° latitude X 2.5° longitude X 20 levels
(207,360 grid points X 2) (doubled time steps)
16 times the "cost"
Exploratory Resolution
1° latitude X 1° longitude X 40 levels
(2,592,000 grid points X 5) (quintupled time steps)
500 times the "cost"
FIGURE 7.2 Illustrative example of the strong demands on computer
resources as a climate model's grid resolution is increased.
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64
In spite of significant climate model limitations, simulations of the
effects of increases in the greenhouse gases permit a number of plausible
inferences to be drawn today with considerable confidence. In most model
studies to date, atmospheric CO2 concentrations have simply been doubled
(e.g., from 300 to 600 parts per million) and then maintained at that
concentration until a new equilibrium climate is established in the
model. Typically, such a model includes just the atmosphere; the only
effect of the ocean included is its effect as a heat reservoir. We
expect such model results to apply reasonably weld to a combination of
CO2 and other trace gases where the total effect on the radiation budget
is equivalent to a doubling of CO2. Moreover, because of the now-
recognized effect of the other greenhouse gases, calculations using
doubling of CO2 are now thought to be relevant (from a societal impact --
perspective) for conditions sometime into the middle of the next century.
In this presentation, I will avoid detailed greenhouse gas scenarios.
Rather, I will emphasize the kinds of expected impacts and my best
estimates of their current scientific uncertainties.
Some of the possible climate responses to increased greenhouse gases
are regarded to be rather well understood; others remain controversial.
Scientific confidence is presented here in general terms. My estimates
of confidence levels based on current models can be interpreted according
to the following guidelines: By ''virtually certain" I mean that there is
nearly unanimous agreement within the scientific community that a given
climatic effect will occur. Here, "very probable" means greater than
about a 9Q percent (9 out of 10) chance, and "probable" implies more than
about a 67 percent (2 out of 3) chance. By "uncertain" in this context,
I refer to an effect that has been hypothesized but for which there is a
lack of appropriate modeling or observational evidence. I list below, in
decreasing order of my current scientific confidence, some important
model-predicted climate changes due to increased greenhouse gases.
(This list is similar to that in National Research Council, 1987.)
o Large stratospheric cooling (virtually certain). A reduction in
upper stratospheric ozone by chlorine compounds will lead to reduced
absorption of solar radiation and thus to less heating. Increased
stratospheric concentrations of radiatively active trace gases will
increase infrared radiative heat loss from the stratosphere. Decreased
heating and increased cooling will lead to a marked lowering of upper
stratospheric temperatures, perhaps by 10 to 20°C (Figure 7.3~.
O Global-mean surface warming (very probable). For a doubling of
atmospheric CO2 (or its radiative equivalent from all the greenhouse
gases), the long-term global-mean surface warming is expected to be in
the range of 1.5 to 4.5°C (see Figures 7.3 and 7.4~. The most signif-
icant source of uncertainty arises from difficulties in modeling the
feedback effects of clouds on climate change. The actual rate of
warming over the next century will be governed by the growth rate of
greenhouse gases, natural fluctuations in the climate system, and the
detailed response of the slowly responding parts of the climate system,
i.e., oceans and glacial ice.
o Global-mean precipitation increase (very probable). As the
climate warms, the rate of evaporation increases, leading to an increase
OCR for page 65
40 \
35 \ ~~x
30 - All Trace Gases—
25
20
15
10
5
o
I 1 1 1
-8 -6 -4 -2
Cot
FIGURE 7.3 Estimate of the global-average temperature change (°C) for
the year 2030 based on projected trace gas trends. 'tCO2 Only" includes
only effects of changing CO2; "All Trace Gases" includes effects of
changing CO2 as well as all the other increasing greenhouse gases.
(Reprinted from Ramanathan et al., 1987.)
in global-mean precipitation. Despite this increase in global-mean pre-
cipitation, local regions might well experience decreases in precipita-
tion.
o Northern polar winter surface warming (very probable). As the sea
ice boundary is shifted poleward, the models predict a significantly
enhanced surface warming in winter polar regions (see Figure 7.5~. The
greater fraction of open water and thinner sea ice is calculated to lead
to an effective winter warming of northern polar surface air by more than
10°C relative to the current climate.
o Reduction of sea ice (verY probable). As the climate warms, total
sea ice is expected to be reduced in response to warming in high lati-
tudes of the Northern Hemisphere. However, new GFDL model results with
fully interactive ocean indicate little warming at Southern Hemisphere
high latitudes over the next century, thus leading to little change in
sea ice cover there (Figure 7.6~. This new model result thus disagrees
with the equilibrium model predictions for the Southern Hemisphere high
latitudes as shown in Figure 7.5.
o Northern high-latitude precipitation increase (probable). As the
climate warms, the increased poleward penetration of warm, moist air may
increase the annual-average precipitation and river runoff in Northern
Hemisphere high latitudes.
O Summer continental dryness/warming (probable). Several model
studies have indicated a marked decrease of the soil moisture over some
midlatitude interior continental regions during summer. This drying is
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66
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LATITUDE
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FIGURE 7.4 Latitude-height cross sections of December-January-February
mean temperature change (°C) for a doubled CO2 world compared to today's
climate for 3 different models. Top, Geophysical Fluid Dynamics
Laboratory (NOAA) model; center, Goddard Institute for Space Studies
(NASA); bottom, National Center for Atmospheric Research. (Reprinted
from Schlesinger and Mitchell, 1985.)
b
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FIGURE 7.5 Latitude-longitude cross sections of December-January-Feb-
ruary mean surface temperature change (°C) due to a doubled CO2 as cal
culated by the three different climate models described in Figure 7.4
(Reprtnted from Schlesinger and Mitchell, 1985.)
OCR for page 68
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30 40 50
YEARS
FIGURE 7.6 Time evolution of zonal-mean, decadally averaged temperature
change (°C) in a GFDL/NOAA coupled atmosphere-ocean model due to a 1.O
percent per year buildup of CO2. The resistance of the southern high-
latitude region to greenhouse warming illustrates the potential of ocean
circulation effects to yield results significantly different from those
indicated in the previous generation of models (from Stouffer, R. J.,
S. Manabe, and K. Bryan, ''On the Climate Change Induced by a Gradual
Increase of Atmospheric Carbon Dioxide,' submitted to Nature).
caused mainly by an earlier termination of snowmelt and rainy periods and
thus an earlier onset of the normal spring-to-summer reduction of soil
moisture. For a comparison of this effect in doubled and quadrupled CO2
atmospheres, see Figure 7.7.
o Rise in global mean sea level (probable). A rise in mean sea
level is generally expected due to thermal expansion of sea water in the
warmer future climate. Far less certain are the contributions due to
melting and calving of land ice. In addition, for the next century there
now exists the possibility of increased snow accumulation over the
antarctic continent. Predictions of actual changes in mean sea level
thus remain difficult and controversial.
o Regional vegetation changes (uncertain). Climatic changes in
temperature and precipitation of the kinds indicated above must
inevitably lead to long-term changes in the~surface vegetative cover.
The exact nature of such changes and how they might feed back to the
climate remain uncertain.
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Representative terms from entire chapter:
climate modeling
90f
6C .
3c
30
60
~ ~—L~
70
To+4
To+2
T (°C)
t 0 25yr 50yr 75yr lOOyr
FIGURE 7.8 Schematic illustration of the greenhouse warming detection
problem. The thick line (Tar) represents evolution of a hypothetical
average gradual greenhouse temperature warming. The thin line (To) is an
assumed undisturbed time-averaged temperature. The dashed line (Tu)
represents the actual temperature variation in an undisturbed climate.
The dotted line (Ta) is the actual fluctuating signal for an earth with
gradually increasing greenhouse gases. Note that it can take many years
to separate the fluctuating greenhouse signal (Ta) from the undisturbed
fluctuating signal (Tu).
O Details of next 25 years (uncertain). The results given above
describe expected changes in equilibrium climate due to hypothetical
large changes in greenhouse gases. In actuality, these gases are
increasing gradually with time. Initially, much of the excess heat is
absorbed into the oceans, perhaps in complex ways we do not yet
understand well. Further, we can expect that natural, decadal-scale
climatic fluctuations due to interactions between the atmosphere and the
oceans will continue to occur. The Midwestern drought in the 1930s and
the high water levels of the Great Lakes in the 1980s are good examples
of such climatic fluctuations. On these shorter time scales, such
natural fluctuations would artificially reduce or enhance the apparent
greenhouse warming signals (Figure 7.8~. Until such decadal-scale
fluctuations are understood or are predictable, it will remain difficult
to diagnose the specific signals of permanent climate change as they
evolve over the next quarter-century. Moreover, detecting climate change
signals becomes even more difficult when smaller regions and/or shorter
periods of time are considered.
71
Even though the above uncertainties are daunting, important advances
have already been achieved in the observation, understanding, and
modeling of the climate system. The current models are capable of
simulating the gross features of geographical and seasonal variations of
the global climate. Furthermore, some of these models have achieved
successful simulations of the very cold climate of the last glacial
maximum and of the extreme temperatures found on the planets. These
overall scientific advances have initiated the current public awareness
of climate change and its potential implications for the future of the
world. This awareness has escalated the need for reliable climate
predictions, accurate assessments of the causes of the actual changes
occurring, and an ability to distinguish human-produced climate change
from longer-period natural variations. Although progress has been made,
as noted above, significant deficiencies remain in the capability of the
scientific community to address these needs.
Much more effort must be expended worldwide toward providing a
climate monitoring and measuring system characterized by careful
instrument calibrations and intercomparisons and a commitment to continue
measurements over many decades. Focused research into climate processes
must be accelerated so that theories can be formulated and reevaluated in
the light of newer information. To reduce climate modeling uncertainty,
it is imperative that climate modeling efforts receive state-of-the-art
supercomputing resources. Additionally, new scientific talent must be
developed to exploit those resources.
Through careful, long-term research on observation, modeling, and
analysis, our scientific uncertainties will decrease and our confidence
for predicting details of the climate system and its changes will
gradually improve. A final, very confident prediction is that the
societal need for accurate and detailed climate predictions will increase
as fast or faster than the scientific community can provide them. The
effort to meet these societal challenges will require the combined forces
of the world scientific community in a sustained effort spanning decades.
ACKNOWLEDGMENT S
I would like to thank Dr. Syukuro Manabe and his group at the
Geophysical Fluid Dynamics Laboratory/NOAA for their contributions to the
perspectives offered here as well as for their unrelenting commitment to
solving the greenhouse gas modeling problem. I am also indebted for the
contributions and cooperative efforts from the other climate modeling
groups at the National Center for Atmospheric Research, Goddard Institute
for Space Studies/NASA, Oregon State University, and the United Kingdom
Meteorological Office.
REFERENCES
Manabe, S., and R. T. Wetherald, 1987. Large-scale changes of soil
wetness induced by an increase in atmospheric carbon dioxide.
Journal of Atmospheric Science, 44, 1211-1235.
72
National Research Council, 1987. Current Issues in Atmospheric Change.
National Academy Press, Washington, D.C.
Ramanathan, V., L. Callis, R. Cess, J. Hansen, I. Isaksen, W. Kuhn, A.
Lacis, F. Luther, J. Mahlman, R. Reck, and M. Schlesinger, 1987.
Climate-chemical interactions and effects of changing atmospheric
trace gases. Reviews of Geophysics, 25, 1441-1482.
Schlesinger, M. E., and J. F. B. Mitchell, 1985. Model Projections of
the Equilibrium Climatic Responses to Increased Carbon Dioxide
Projecting the Climatic Effects of Increasing Carbon Dioxide.
DOE/ER-0237, U. S. Department of Energy, 80-141.
.
