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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

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l I ~ . rn r O ~ OF ~ G) G) ~ z 63 ADVECTION THE - ODYNAMICAL ~ ~ EQUATION EQUATION ~ OF MOTION _ ~ DENSITY WNN, ~ < rn o RADU RATION | MOISTURE EQUATION TRANSFER 1 - - - OF WATER VAPOR ~ l ~ q~0~ , ~ ~ ~ , , 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 20C (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 4.5C (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

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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 10C 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 GFDL, 2xco2-lxco2 20 - 1.2 25 55 - - L~ 121 ~ Lo ( \ ~''''\..\ ~ O- ,5 ,1~x :.~: :~.: A; :.: :` 1 , `::::: A\\\\\\\\' -1013 90N 70 50 30 1 ON 1 OS 30 50 70 90S G ISS, 2 XCO 2-1 xCO 2 30 25 15 O- 90N 70 50 30 30 25 -12 -1013 1 ON 1 OS 30 50 70 90S NCAR, 2Xco2 - 1XCO2 1 . 1 1 1 20 15 10 O ~ <1 , , ~ , ~ it \\\\\\4 1013 90N 70 50 30 1 ON 1 OS 30 50 70 90S LATITUDE -55 ~ -121 em Lo 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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90N ~ 70p 50r 30-1 ION 10 - 30 - 50 . 70- 90S 90N ~ 70- .. 50 - 30- lON - 10 - ~n 67 GFDL, 2Xco2-lxco2 .. ...... .... ~ .. . . ~6~_~ ~2~ ~ ~~ 'a ~~::~ a_ t~ <~C ~ 4 O " I: . _~_ ~ 4_~_== ~_ .~J... :-:: ::::::: a..-. ~ : : .: : : :- 6 : : : : . . : : : ..: . :::::: : : : : : : : : . . . . . . . . ~ ; ~ r ::::::::::: . :::: ~4 .::::::: :~. :::::::::: ~: :~:::::::::: :: :_ :::::::::: -.:~ 4~. :::::::~6.~ : _ ~ ~ ~ ~2~::::: : :6 ................ ~ ~ ::: ~ 2 Ye:::::: . :4 ................... , ~.; ; ~ W::::::::::::::::::::::: ::::::::::: ::::: 30W 0 30E 60 90 120 150 180 150 120 90 60 30W 0 3 E W(,7 ~= ~ ~=~ ~ 26 ~ ~ >~ GISS, 2Xco2-lxco2 ; I ':.>''1' " ~ 50- ~ ~ 4~ ;;;; .-; ;; ::::::::: .: 70 90S 30W 0 30E 60 90 120 150 180 150 120 90 60 30W 0 31 ~E NCAR, 2Xco2-lxco2 90N- ~ _ i2 2222 ' 2 '' ' ;2 ;A2; '' 2' ~ _ t 70 50 . 30 ION 10- 30- 50- 70 - 90S~ \~4: ~ ~,. ~ ~ ^4 - 2~ ~ ~ ~ ~ ~) W~ 1~ :~, : :.:.-.;.:.: ; ; ~ : , :.: ~2 .. , ' ~ 30W 0 30E 60 90 120 150 180 150 120 90 60 30W 0 3 E 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.)

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- - 30 _ EQ _ 30 _ 68 \ 0.5 1 '1 ' ~ 1 ~ ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 'I ~ ~ ~,,. ~ 2.2 -.~ 2 2.~ ~~ '''I'm A ,' , , / - ~ - ~ - - - ~ ~ ~ t--2-2.-2..2...~ 2.-..2-~-2.'~.2..-.~.2...~..~ ~.~.~ ~ .......... ~::::::::::::::::-:::.:.:,:.:-: :,:~-:,: :-:: :-: :,:,::: :-::: hi' 'ah: :,:.:2:.:,: :~-: :-:2:- t::::::::: :::::::: ~ .. ... .... . .~. \:::::::::::~::::::::::~ ~ 2 ~ ~. ) ~ .......... ~ , , . . ~ , , . a /:::::::::::::::~:::::::::~ ~ ~ / ......... ~ he. .. ~ A::::::::::::::::::: :::::::::~ ~ .... .................. ~ t. - .  ............ 1 ::::::::::::::::~:::::::::::~ ~ : I :::::::::::::::t::::::::::::::~ - - . ~ 1 \ - - . ~ ~,,:::::: :.:: .,, ~ , ~ - : . 2 0 . ~ 1 \::::::::::::::::~::::::::::::: ~.~ ~ \::::::::::::::::::~:::::::::::::::~.~ .:~. I ~ - - - - - - - - - - - - - - - - - - - - - -~1 ~ - - - - ~ ~ ~ ~ :,: 1 ~ .. .. : arm:::::::::::: :N .................. - 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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90f 6C . 3c 30 60 ~ ~L~ OCR for page 62
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.

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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.

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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. .