Cosmic conclusions from climatic models: Can they be justified?

ICARUS 41, 456-469 (1980)

Cosmic Conclusions from Climatic Models" Can They Be Justified? S T E P H E N H. S C H N E I D E R AND S T A R L E Y L. T H O M P S O N 1 National Center for Atmospheric Research, .2P.O. Box 3000, Boulder, Colorado 80307 Received M a y 7, 1979; revised A u g u s t 6, 1979 Climatic models are increasingly being used to a n s w e r " c o s m i c q u e s t i o n s " such as the possibility o f an ice-covered Earth or a r u n a w a y g r e e n h o u s e effect, or to e x a m i n e the coevolution of climate and life. C o n c l u s i o n s from t h e s e models on such issues, of course, rest on the physical parameterizations o f the models. Some of the basic parameterizations are reexamined quantitatively, and it is concluded that presently believed uncertainties in these parameterizations lead to an order-of-magnitude uncertainty in estimates of the sensitivity of the present E a r t h ' s climate to external forcings (like a change in solar constant). However, seasonal simulations with present Earth models suggest that estimates of the overall sensitivity of the climate to external forcing m a y be narrowed (over decadal time scales) to, perhaps, a factor of 2. But the effects of glaciers, continental locations, a n d atmospheric composition, all of w h i c h can change on geological time scales, further e n h a n c e the uncertainties in long-term climatic sensitivity estimates from state-ofthe-art models. But it is precisely these long-term estimates of climatic sensitivity which support quantitative conclusions on, for example, the possible existence of continuously habitable zones around m a i n - s e q u e n c e stars. We believe that those who draw cosmic conclusions from climatic models should at least attempt to bracket the final results by repeating their calculations over a plausible range of uncertainty in basic model parameterizations. t

LIST OF SYMBOLS

S /3 T Fi~r

tr ap So A B f~ f ~b

Solar constant Global climatic sensitivity parameter Surface air temperature Terrestrial infrared radiation to space Planetary emissivity Stefan-Boltzman constant Planetary albedo Present value of the solar constant Constant in t e m p e r a t u r e / i r parameterization Constant in t e m p e r a t u r e / i r parameterization Fraction of a planet covered by clouds T e m p e r a t u r e / a l b e d o feedback coefficient Latitude

1 Presently at University of W a s h i n g t o n , Departm e n t of A t m o s p h e r i c Sciences AK-40, Seattle, W a s h . 98195. 2 T h e National Center for A t m o s p h e r i c R e s e a r c h is s p o n s o r e d by the National Science F o u n d a t i o n .

R F

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I N T R O D U C T I O N : R E C E N T I N T E R E S T IN CLIMATE MODELING

Climatic modeling is coming of age. What was hardly a defined field (e.g., see Chapter 6 of SMIC, 1971) only a decade ago grew in scope very rapidly during the mid-1970s (e.g., see Schneider and Dickinson, 1974, or GARP, 1975) to the point that the field, going into the 1980s, can claim literally hundreds of adherents at dozens of institutions (e.g., see GARP, 1979). Moreover, no longer are climatic models built primarily as tools to improve the understanding of climatic phenomena, but they are increasingly being asked to shed light on two bolder fundamental questions: (1) what is the impact of human activities on climate, and (2) how have climate and life coevolved on Earth (and a corollary: how might climatic evolution on other planets offer conditions

456 0019-1035/80/030456-14502.00/0 Copyright © 1980by AcademicPress, Inc. All rights of reproduction in any form reserved.

Time Thermal inertia coefficient Meridional energy flux Latitudinal and seasonal incoming solar radiation

COSMIC CONCLUSIONS, CLIMATIC MODELS conducive to some forms of life)? Indeed, any answers coming from climatic models about these questions, particularly the second one, could well be termed, as we have, " c o s m i c conclusions." H o w justified any such conclusions might be coming from state-of-the-art climatic models, however, is the question to be addressed here. We will begin by briefly and selectively reviewing a few of the cosmic conclusions from early climatic modeling efforts. Then we turn to a review of the factors whose influences need to be modeled properly if conclusions from climatic models are to be reasonably credible. We finish with some " c o s m i c conclusions" of our own on the justifications for using stateof-the-art (or likely near-future) climatic models to study cosmic issues such as the coevolution of climate and life. M O D E L I N G THE SENSITIVITY OF THE E A R T H ' S CLIMATE

The Ice Catastrophe A basic problem that has occupied most climate modelers is simply: What is the sensitivity of the Earth's climate to perturbations in boundary conditions external to the atmosphere? These could include a change in solar " c o n s t a n t " (S); atmospheric composition; heat input from human activities; land-sea distribution; orbital elements which govern the geographic and seasonal distribution of incoming solar radiation; or the surface properties of land, ice, or sea. The simplest calculation to carry out with a model is the response, fl, of the global average surface temperature, T, to a unit change in S. Budyko (1969) and Sellers (1969) independently published papers with the same dramatic conclusion: /3 is a very sensitive, nonlinear function of S. Whereas a continuous, but small, decrease in S (~1.5%) would cause a continuous decrease in T, any minute decrease in S below a threshold of about 1.5-2% would lead to a discontinuous climatic response: an ice-

457

covered Earth! [Furthermore, as North (1975) or Gal-Chen and Schneider (1976) noted, this glaciated Earth would remain so unless S were to be increased by tens of percent over present.] This "ice c a t a s t r o p h e " from these prototypical climatic models was the cosmic conclusion that contributed to the impetus for the dramatic growth noted o v e r the 1970s in the number of climatic m o d e l s - and modelers. Later on we will digest the findings over the decade since the work of Budyko (1969) and Sellers (1969) [e.g., see T h o m p s o n and Schneider (1979) for an updated list of references] in order to reexamine the justification for the ice catastrophe, or any other cosmic conclusions that depend on it. Faint Early Sun Paradox It has been noted theoretically (e.g., Ulrich, 1975) that the Sun, as for most mainsequence stars, gradually increases in luminosity with time, which would mean that S was thus some tens of percent less a few billion years ago than it is today. A paradox then arises: How could both S have been that low and the Earth have escaped the ice catastrophe? Sagan and Mullen (1972) suggested the answer might lie in the composition of the primordial atmosphere. That is, the added " g r e e n h o u s e effect" of more (then than now) ir-opaque ammonia in the atmosphere could permit both a lower S and a nonglaciated Earth, even if the fl of the B u d y k o or Sellers models were accurate. Henderson-Sellers and Meadows (1977) and Owen et al. (1979), for example, recently agreed with the concept of Sagan and Mullen that ir opacity of the primordial atmosphere was higher than it is now, but argue that CO2, rather than ammonia, was the important " g r e e n h o u s e g a s . " Regardless of the outcome of the debates o v e r the ice catastrophe results, the faint early Sun paradox or the primordial atmospheric composition, one prominent and obvious conclusion clearly emerges: climatic models must consider the nature of

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the climatic system and its boundary conditions (e.g., atmospheric composition and solar irradiance) for the time at which the model is applied for climatic simulation. A model (e.g., Budyko, 1969, or Sellers, 1969) derived from modern conditions may not be applicable to past times when the conditions were vastly different. CLIMATE MODELING OF ATMOSPHERIC AND CLIMATIC EVOLUTION

A n u m b e r of authors have recognized the importance of the evolution of the composition of a planet's atmosphere in the evolution of its climate. For example, Rasool and de Bergh (1970) investigated relationships among the p l a n e t - S u n distance, the evolution of planetary surface temperature, and ir opacity of the atmosphere and the feedback effect of these on the evolution of atmospheric composition and climate. More recently, Hart (1978, 1979) and Chen (1978) have made similar calculations. Although all three of these studies use different modeling assumptions (e.g., in radiative transfer calculations or cloudiness variations) they all consider the evolution of the composition of a planetary atmosphere as crucial to their results. This is, of course, necessary for credible conclusions. However, is it sufficient? In view of the uncertainty in the time evolution of actual planetary atmospheric compositions (compared to those assumed or computed in each respective model), there is reason to question specific results. And, perhaps even more importantly, the atmospheric composition is not the only factor in the climatic system or its boundary conditions which could evolve in time. Surface composition and optical properties, cloudiness, orbital elements, orographic features, or solar irradiance could singly, or in combination, have varied significantly over geologic time. [See Pollack (1979) for a review of theories of climatic evolution on the terrestrial planets.] Cosmic conclusions have been extracted from evolutionary climatic models (e.g.,

Hart, 1978, 1979) which attempt to simulate changes on this 109-year time scale. H o w justified, then, can the results of these pioneering studies be in the light of (1) what is known (and unknown) about the properties of the present Earth's climate, and (2) the likelihood that many of the factors which could contribute to vastly different climatic conditions are not i n c l u d e d - - o r are included improperly--in climatic models? CONTINUOUSLY HABITABLE ZONES

Here we will concentrate in more detail than above on the " c o s m i c conclusions" from models regarding the habitability of Earth for terrestrial life. One may assume there is a certain habitable zone around a main-sequence star of a given luminosity (Huang, 1959, 1960). For our purposes, the solar habitable zone may be defined as that region in which a terrestrial planet can retain a significant amount of liquid water at its surface, assuming the atmospheric pressure is great enough to allow it. The extreme climatic conditions which would prevent a habitable Earth are then the cases when all the water has been evaporated from the surface (the runaway greenhouse), or when the Earth has completely glaciated (the ice catastrophe). The evolution of solar luminosity has presumably caused the center of the habitable zone to move outward from the Sun. Thus the continuously habitable zone (CHZ) of Hart ( 1978, 1979) can be narrower than the habitable zone at a given time. It is doubtful that a unique CHZ can be defined for a given star, since the CHZ width must depend on the characteristics of particular planetary climatic systems and boundary conditions. In addition, credible extrapolation of CHZ results from Earth models to other stellar systems requires that it can be shown that a significant number of planets which form around mainsequence stars are remarkably similar to the primitive Earth. Rasool and de Bergh (1970) concluded that a runaway greenhouse would have likely occurred on Earth had the planet

COSMIC CONCLUSIONS, CLIMATIC MODELS formed closer than - 0 . 9 A U to the Sun. H a r t (1978), using a more physically comprehensive E a r t h model, estimated that the C H Z around a solar-type star extends from roughly 0.95 to 1.01 AU. H a r t (1979) applied his a t m o s p h e r i c evolution model to other main-sequence stars and found, as a c o n s e q u e n c e of the ice c a t a s t r o p h e , that no C H Z exists about most K or M stars (the Sun is a G2). F u r t h e r m o r e , stars greater than 1.2 solar masses induced a r u n a w a y greenhouse in the model planetary atmosphere. The results of these thought-provoking models are considerably uncertain due to, for e x a m p l e , crude parameterizations, the possible omission of relevant p r o c e s s e s , and the lack of good data for the early Earth needed to verify the models' results. In the r e m a i n d e r of this p a p e r we will review results which help to bracket the uncertainty in some basic p a r a m e t e r s which determine the C H Z , uncertainties arising from our incomplete knowledge of the climatic c o m p o n e n t alone. We begin b y discussing E a r t h ' s present climate sensitivity to solar constant changes as estimated from state-of-the-art climatic theory. Theory m a y be aided s o m e w h a t by observations of climatic " s y s t e m s e x p e r i m e n t s . " But e v e n if the p r e s e n t climatic sensitivity were well determined, p r o b l e m s imposed by the evolution of the surface and atmospheric composition would remain formidable. As an example of a long-term complicating factor, we discuss some possible climatic consequences of continental drift. We conclude by suggesting that estimates of the C H Z should, at a minimum, be presented so as to bracket the e x t r e m e possibilities resulting from simulations using plausible e x t r e m e values of uncertain basic p a r a m e t e r s in the models. PRESENT CLIMATIC SENSITIVITY TO EXTERNAL FORCING RADIATIVE EFFECTS In o r d e r to determine a C H Z , we must be able to c o m p u t e the complete time evolu-

459

tion o f the E a r t h ' s surface t e m p e r a t u r e . A less ambitious, but still relevant, preliminary task is to determine the sensitivity of the E a r t h ' s present equilibrium climate to solar constant changes. As a first approximation, it is possible to consider only radiative effects. The simplest model of equilibrium surface t e m p e r a t u r e is the radiative balance F~ = •trT 4 = (S/4)(1 - ctp),

(1)

where T is the t e m p e r a t u r e , • is a constant effective emissivity, tr is the S t e f a n Boltzman constant, S is the " s o l a r cons t a n t , " and ctp is the planetary albedo. As defined in Schneider and Mass (1975), a global climatic sensitivity p a r a m e t e r is dT

/3 --- S0 ~-g,

(2)

where So is the present solar constant. F r o m (1), for the present Earth case with no internal feedbacks (i.e., • and a o are constant), /3 is - 7 0 ° K (i.e., a 1% change in S p r o d u c e s a 0.7°K change in 7). I f • or otp could change with T, these f e e d b a c k effects could radically change/3. A very important positive temperature/radiation f e e d b a c k results from the increase in atmospheric water v a p o r with increasing temperature. F o r the present Earth this effect m a k e s outgoing terrestrial radiation (Fitr) more nearly a linear function o f the s u r f a c e t e m p e r a t u r e than (1) would indicate. Figure 1, from Warren and Schneider (1979), shows the outgoing terrestrial infrared irradiance as m e a s u r e d by satellite versus the o b s e r v e d surface temperature. ( F r o m here on, T refers to air t e m p e r a t u r e at the surface.) I f we let Fi~ be a linear function o f T, F~tr- = A + B T , the climatic sensitivity is (see Appendix of Schneider and Mass, 1975) inversely proportional to B: /3 = (S0/4)[(1 - a p ) / B ] .

(3)

The w a t e r v a p o r and other f e e d b a c k s implicit in the ir observations from satellites yield a B which, when used in the climate

460

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latitude zones) of zonally averaged outgoing infrared irradiance, F~, m e a s u r e d by satellites (Ellis and Vender Haar, 1976) plotted against c o r r e s p o n d i n g values of surface air t e m p e r a t u r e , T. The straight line is a least-squares fit to the data. Note that physical proc e s s e s in the real a t m o s p h e r e lead to a fairly linear d e p e n d e n c e of FL~ on surface temperature, as opposed to the /~ relationship of simple theory. (Source: Warren and Schneider, 1979.)

lar zenith angle (Cess, 1976). Figure 2 shows the annual variation of ap at several latitudes, as m e a s u r e d by satellite (Ellis and V e n d e r H a a r , 1976) and calculated by T h o m p s o n (1979) using C e s s ' a l b e d o - z e n ith angle relationship. More than half of the annual variation in ctp arising from this calculation is due to the solar zenith angle change. The net effect of a change in cloud amount on the global radiation balance remains something of a c o n t r o v e r s y . Cess (1976) estimated no net effect, but the observations of Ellis (1978) indicate that the influence on planetary albedo p r e d o m i n a t e s o v e r the influence on Fi~ for the present climate. Cess and R a m a n a t h a n (1978) explore possible reasons for this discrepancy and evaluate the results of a n u m b e r of OBSERVED AND COMPUTED ALBEDO

models of Schneider and Mass (1975) or Cess (1976) or Warren and Schneider (1979), increases /3 to -150°K. But as the latter two authors point out, the estimate of B obtained from satellites varies considerably as a function of latitude and season, raising questions about the functional form of the parameterization. When the effects of cloudiness are explicitly included, the climatic sensitivity bec o m e s harder to determine. Clouds act to decrease F+tr relative to a cloudless sky since their tops usually radiate at a lower t e m p e r a t u r e than the surface. R a m a n a t h a n (1977) found the effect of a given amount of clouds on Fi~ to be very nearly a linear function of the t e m p e r a t u r e difference between the cloud top and the E a r t h ' s surface. Thus, in a model calculation /3 can vary by a factor of about 2, depending on the assumptions one m a k e s concerning cloud top t e m p e r a t u r e changes, let alone changes in cloud amount. E x c e p t o v e r highly reflective surfaces, clouds will increase the planetary albedo. F u r t h e r m o r e , the albedo of clouds appears to increase significantly with increasing so-

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FIG. 2. The annual variation of E a r t h ' s zonally a v e r a g e d pl a ne t a ry albedo as o b s e r v e d by satellites (Ellis and V e n d e r Haar, 1976) and as c o m p u t e d by a mode l a c c ount i ng for variations in surface albedo, cloudiness, and solar zenith angle. Cloud albedo is a s s u m e d to obey the a l b e d o / z e n i t h - a n g l e relationship suggested by Cess (1976). More than half of the a nnua l variation of the c o m p u t e d albedos is due to solar zenith angle changes. Most of the remaining c o m p u t e d var i a t i on is a result of surface albedo changes. (Source: T h o m p s o n , 1979.)

COSMIC CONCLUSIONS, CLIMATIC MODELS other researchers. In any case, the uncertainties in basic parameters (such as cloud or surface albedos or cloud top heights) are at the level of several percent or more, rendering any estimates of cloud amount/global radiation balance effects uncertain to a considerable extent. Regardless of our ability to understand the direct radiative influences of prescribed changes in clouds, we must still predict such quantities as cloud amount and cloud top temperature. There appears to be no obvious way of doing this at present except by using highly resolved dynamical general circulation models (GCMs). Even in these models, the cloud parameterizations are at best highly empirical, limited largely by the coarse grid resolution (relative to the scale of real clouds) and lack of verifying observational data. Experiments with at least one GCM (Schneider et al., 1978) reveal that no simple parameterizations of the feedback processes between cloudiness and surface temperature are available yet for general use in lower-resolution climate models (such as those used so far to estimate CHZs). Yet, in his CHZ studies, Hart (1978, 1979) assumes arbitrarily that the fraction of the planet covered by clouds, f~, is proportional to the total mass of water vapor in the atmosphere. In turn, the atmospheric water vapor partial pressure, given an available surface reservoir of H20, is approximately an exponential function of the surface temperature through the Clausius-Clapeyron relationship. The consequence is that f~ varies from about 0.25 at 280°K to 1.0 at 300°K in Hart's model. (This would certainly not produce a realistic cloudiness profile from equator-to-pole for the present Earth.) This strongf~(T) dependence is, clearly, highly debatable. The empirical evidence does not support such a parameterization (Cess, 1976), and dynamical modeling studies (e.g., Roads, 1978; Schneider et al., 1978; Wetherald and Manabe, 1975) indicate a slight d e c r e a s e of f~ with increasing global temperature. Fur-

461

thermore, while Hart explicitly includes the effect of fe on the planetary albedo, the influence of cloud amount on Fi'r is incorporated only by tuning the infrared parameterization to the present conditions (i.e., OFi'~/Of~ = 0). This is an extreme assumption in view of the empirical evidence and theoretical reasoning mentioned earlier. [Owen et al. (1979) also point out the strong negative feedback inherent in Hart's radiation assumptions.] The net result of these parameterizations is a strong negative cloud amount/surface temperature feedback which stabilizes Hart's model, particularly against the ice catastrophe. Indeed, if more plausible assumptions of cloudiness change and radiative effects were made, the model would appear, presumably, to predict an ice-covered Earth at present. Thus, this potentially crucial factor in determining climatic sensitivity to external forcing is not based on verified assumptions. Any conclusions about CHZs will, thus, rest on these assumptions. In summary, state-of-the-art theory cannot yet resolve whether cloudiness changes could present positive, negative, or neutral feedback effects on surface temperature variations. Of course, our inability to confidently assess the influence of changes in cloudiness on climate does not require that the influence be overwhelming; it merely implies that it could well be a most serious deficiency of present models. Another important feedback process is the coupling of surface temperature and surface albedo. This positive feedback is operative when snow and ice cover increases with decreasing surface temperature. Thompson (1979) calculates that somewhat less than half of the annual variation in ctp shown in Fig. 2 is a result of seasonal snow cover and sea ice variations. Recently, Cess (1978) proposed that major long-term (greater than decades) changes in vegetation cover associated with long-term temperature changes create an analogous positive temperature feedback in lower lati-

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SCHNEIDER AND THOMPSON

tudes. He based his proposal on the field evidence that deserts were more extensive during ice ages. Simple climate models may approximate these effects by making ao a nonlinear function of the surface temperature (see Fig. 3 caption). Figure 3, from Warren and Schneider (1979), illustrates the variation in global climatic sensitivity resulting from various choices of the coupling of temperature to Fi~ and ap. B is as defined earlier for Fi~ and f i s - O o t J O T ( f o r T < 10°C). The latitude of the edge of permanent ice, as deduced from a zonally averaged climate model, is plotted against the percentage change from the 90 80

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present value of the solar constant. Two types of climatic sensitivity can be seen./3, as defined by (2), is approximately proportional to the slope of the curves at the point of no change in S. This is a l o c a l s t a b i l i t y (more aptly, a local sensitivity) since it is only applicable to small deviations from the present climate. The g l o b a l s t a b i l i t y parameter is the decrease in S necessary to bring the ice line to the equator. The different values of the feedback coefficients (f and B) in Fig. 3 were chosen (see Warren and Schneider, 1979) to indicate a plausible range of uncertainty in present theoretical estimates of /3 and global stability. The important thing to note is that, even for the present climate, including uncertainties only in radiative processes, estimates of global stability parameter can vary from 2 to 20% or more.

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Fie. 3. The global mean climatic sensitivity and stability of a zonally averaged energy balance climate model as a function of the strength of two radiation-temperature feedbacks: (1) surface temperature/planetary albedo coupling, and (2) surface temperature/outgoing infrared coupling. Global stability is defined as the percentage decrease in solar constant (from the present value) required to bring the edge of permanent ice to the equator. Local stability (or sensitivity) is proportional to the slope of the lines at the point of no change in solar constant (i.e., the global climatic sensitivity to small perturbations in solar constant). The values of B are plausible coefficients used in the empirical formula for outgoing infrared, F~r = A + BT (see Fig. 1). f i s the albedotemperature coefficient for Sellers" (1969) planetary albedo parameterization. (Of the two values given, = 0.004 is now thought to give a better simulation, although the validity of the parameterization for climatic change experiments is questionable.) Larger values of B (or jr) indicate a stronger dependence of outgoing infrared irradiance (or planetary albedo) on surface temperature. Note that these plausible values of the parameters generate a wide range of climatic sensitivities. (Source: Warren and Schneider, 1979.)

The assumption of radiative balance at all latitudes cannot, o f course, be justified in estimating the global climatic sensitivity. N o r can the effects of the atmospheric and oceanic circulations necessarily be averaged out by considering only global means. It is well known that permanent ice on Earth would exist far equatorward of its present position were it not for the ameliorating poleward transports of heat by the atmosphere and oceans. While it is possible to estimate these meridional fluxes explicitly through numerical integration of the three-dimensional, time-dependent hydrodynamical equations for up to several simulated years, integration b e y o n d decades exceeds the capability of present computers. For this reason the results of most climate models depend on the assumptions made in parameterizing the dynamical transports of heat in terms of surface temperature and its gradient. The scope of this paper does not permit an extended discourse on this important problem, but a few examples of circulation effects are in order. The reader is referred to Oort (1971) and Oort and Vonder Haar (1976) for a discussion of

COSMIC CONCLUSIONS, CLIMATIC MODELS observations of the present heat transports. A review of the theory of the atmospheric general circulation is given in Lorenz (1967). The poleward heat flux is considered to act usually as a negative feedback. For example, if the polar regions cool or the tropics get warmer, an increased poleward flux of heat is believed to arise, thereby driving the system toward its previous state. It is not clear how strong this climatic restoring force is, although the increased poleward heat flux in winter relative to that in summer provides evidence that it does exist. It is not impossible, however, to imagine situations in which circulations could act to amplify temperature changes: standing planetary-scale waves in the atmospheric circulation may provide conditions favorable for the equatorward extension of snow and ice; a convectively stable atmosphere over extensive snow or ice fields may decrease the meridional heat flux by large atmospheric transient eddies, etc. With regard to present climate sensitivity, the effect of poleward heat transports is to reduce /3 by decreasing the extent of polar ice. However, the effect of transports on global stability is less clear. There is the possibility that the circulations may have a strong nonlinear influence on the extent of permanent ice. The plot of ice line versus change in S might level off a bit at some subtropical latitude if the ice edge advance were held back by intensified meridional heat transports out of tropical latitudes--at least until the tropics cooled sufficiently to permit ice cover. This "stability ledge" (Lindzen and Farrell, 1977) would increase the global stability even though its presence might not be felt during smaller climatic changes. On the other hand, reduced meridional transports could, in some circumstances, insulate the tropics from cooling felt in higher latitudes, thereby increasing global stability. State-of-the-art parameterizations of heat transports cannot yet be verified quantitatively over the wide range of variations for changes in S on Fig. 3 (i.e.,

463

tens of percent). The above uncertainties in the dynamical transport parameterizations of simple zonal climate models can only be compounded with the radiative ones indicated in Fig. 3, as discussed by Warren and Schneider (1979). Any cosmic conclusions drawn from climatic models will rest on these parameterizations. SYSTEMS EXPERIMENTS: FORCING, RESPONSES AND TRANSFER FUNCTION Earlier we discussed one route to estimation of the climate sensitivity parameter/3, namely, simulation with climatic models based on a s s u m e d (or semiempirical) values of the parameters which determine the strength of the climatic feedback processes (which, in turn, determine /3). However, the integral effect of all such feedback processes still cannot be well verified, given the uncertainties in the state-of-theart of both climatic models and supporting observational data (e.g., see the discussion in Schneider et al., 1978). This inability of theory alone to provide confident (i.e., much better than order-of-magnitude) estimates of the sensitivity of the present climate to unit external forcing leads to the search for an empirical way of checking model estimates of/3, what could be termed "climatic systems experiments." We define systems experiments as cases where large external forcings and a statistically significant climatic response can both be documented empirically. These geophysical "experiments" can, by analogy to systems analysis, help to identify a "transfer function" (i.e., the nature of the climatic system which present theory and observation inadequately describe). (In linear theory we might similarly look for the Greens' function for the climate system.) A transfer function can be estimated in practice by varying the parameters which control climate sensitivity (e.g., ap or F~) so as to reproduce in a model the observed climatic response to a known climatic forcing.

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The process for a zonal energy balance model (e.g., see Thompson and Schneider, 1979) is illustrated by the equation

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[div F] R '

(4)

where div F represents net heat transport out of a latitude zone, 4~, and R is the thermal inertia of each zone. In this example, Q(~b,t) represents the seasonal solar forcing and OT/Ot the seasonal temperature response (both of which are well known). The transfer function, then, is made up of the parameters which relate the terms in each of the square brackets in (4) to the dependent (T) and independent (th,t) variables in (4). But there are at least three separate feedback terms in the square brackets (plus the need for R to be specified or calculated), and it is likely that one could reproduce the response, OT/Ot, to a known forcing, Q(~,t), with a nonunique set of plausible parameterizations which comprise the transfer function. Therefore, systems experiments are of limited usefulness in deriving or verifying individual parameterizations which determine a climate model's sensitivity. H o w e v e r , systems experiments are important for verifying the overall climatic sensitivity of models to a given external perturbation. H o w e v e r , unless parameterizations are individually validated, a climate model may produce the right climatic sensitivity for certain kinds of external forcings, but the wrong sensitivity if those same parameterizations are used in experiments with other kinds of external forcings. We will next describe some of these systems experiments briefly. EXAMPLES OF SYSTEMS EXPERIMENTS

The Seasonal Cycle We already mentioned that the seasonal cycle is an excellent example of a clear external forcing and a statistically

significant climatic response. F o r example, it is known that the amplitude of the seasonal cycle of surface temperature in the northern hemisphere (NH) is about 14°K, whereas it is only 6°K in the southern hemisphere (SH). It is apparent from simple physical considerations--reconfirmed recently by modeling experiments (e.g., see North and Coakley, 1979, or Thompson and Schneider, 1979)--that the larger ratio of water to land in the SH relative to that in the N H leads to a value of thermal inertia in the SH larger than that in the NH. The larger R in the SH results in greater seasonal heat storage and smaller seasonal temperature cycle amplitude than those for the NH. This example points out that the amplitude of the seasonal cycle of temperature in a hemisphere could be simulated correctly if, say, thermal capacity were overestimated but the strength of temperature-albedo feedback processes were underestimated. The converse, or other combinations of compensating errors in estimates of transfer function parameterizations, could be easily suggested. What is needed, then, is enough independent observational data to fix parameterizations for the terms in square brackets of (4) within fairly narrow ranges of uncertainty. Also, data for parameters like R are needed as well. Data such as those plotted on Figs. 1 and 2 can clearly help to narrow the range of uncertainty in the parameterizations of these feedback processes. After this is done, independent systems experiments are needed to help verify the overall climate sensitivity of models.

Volcanic Dust Veils It has long been suspected that the stratospheric dust veils following explosive volcanic eruptions could affect climate by interfering with radiative transfer between the Earth and space [see Mass and Schneider (1977) for a recent list of references).] H o w e v e r , the existence of a potential volcanic signal in long-term climatic statistics has been controversial be-

COSMIC CONCLUSIONS, CLIMATIC MODELS cause the magnitude of such hypothesized signals is comparable to the amplitude of the inherent interannual variability (or noise) of the climate. Even so, by composite techniques (i.e., superposed epoch analysis) it can be shown (e.g., Mass and Schneider, 1977) that a cooling of a few tenths of a degree Celsius can be detected in a few dozen long-term temperature records. H o w e v e r , because of the weak signal-tonoise ratio from the volcanic events and the uncertainty in quantitative data on the radiative perturbations from historical dust veils, Mass and Schneider (1977) concluded cautiously that only order-of-magnitude insights for climatic sensitivity analyses could be extracted from these volcanic systems experiments. A few more major volcanic eruptions (where the radiation perturbations are well documented) are needed before the observed climatic response can be usefully compared to global climate model calculations. Orbital E l e m e n t Variations

Orbital element variations cause a perturbation to the latitudinal and seasonal distribution of insolation but only a negligible change in global annual solar constant. That these perturbations could cause Quaternary glaciations is commonly known as the "Milankovitch hypothesis." Recently, spectral analyses of the time series of oxygen isotope ratios in two ocean sediment cores (Hays et al., 1977) show some power at frequencies near the three periodicities of Earth orbital element variations (i.e., 100,000, 40,000, and 22,000 years). Although this evidence is only statistical, it has motivated recent attempts to model physically possible connections between the insolation perturbations and the hypothesized glacial/interglacial response. This Milankovitch climatic change experiment has been performed recently with a variety of energy balance models (e.g., Suarez and Held, 1976, North and Coakley, 1979; Schneider and T h o m p s o n , 1979). In these cases similar results were obtained:

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The simulated temperature record in the northern hemisphere led the observed record by some 5000 years, and the amplitude of simulated glacial/interglacial transitions was considerably less than the observed amplitude. These modelers have all speculated that the phase error could easily be attributed to the lack of explicit continental ice sheets in their models, since the time scale to change appreciably the extent of continental glaciers in the northern hemisphere is generally thousands of years. In fact, a simulation by Pollard (1978), which combined a zonal energy balance model with an ice sheet model, confirms that the phase error betwen simulation and observation can be reduced by inclusion of an interactive ice sheet model. But the weak glacial/interglacial signal produced by the models is more difficult to rationalize than the phase error. For example, Cess (1978) has argued that slow vegetation changes occurring on time scales of centuries or more could change surface albedos enough to cause about a factor of 2 underestimate in the amplitude of the glacial/interglacial signal produced in simple Milankovitch-forced energy balance models. Furthermore, the direct effects of radiation changes (from orbital element variations) on snow melt could alter albedo and thus temperatures on long time scales. Therefore, a model which performs well in a seasonal simulation cannot necessarily be trusted to estimate reliably climate sensitivity, fl, to forcings occurring over longer time scales, for example, centuries. Moreover, if the influence of deep ocean heat storage or continental glacier effects on surface albedo, orography, or evapotranspiration are considered, it is quite possible (perhaps likely) that a/3 which agrees with short-term (i.e., up to a few years) systems experiments (or derived from short-term theory) could be an order of magnitude different than /3 would be for forcings occurring over millennia. And, if even longer time scales are to be considered, then interactions among atmosphere, oceans, ice and

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lithosphere (e.g., see Sergin, 1979) could readjust the sensitivity estimates once again. Climatic modeling is only beginning to identify quantitatively the potential importance of processes occurring o v e r a spectrum of time scales to the estimates of climatic sensitivity on these scales. CONTINENTAL CONFIGURATION: A COMPLICATING FACTOR ON GEOLOGICAL TIME SCALES In the last section we showed the large uncertainty in the estimates of global climatic stability without even considering changes in surface conditions or atmospheric composition on geological time scales (e.g., >107 years). It is now well accepted that continental shapes and locations have changed o v e r geologic time. As one example of a long-term complicating factor, we will discuss next some possible climatic effects of changes in continental configuration. The grossest measure of l a n d - s e a distribution is the fractional area of the globe covered by land. This quantity has varied by 20% in the past 180 my (Barron et al., 1979). A direct radiative effect exists since oceans generally have a lower albedo than land surfaces. An increase in total ocean area should thus decrease the planetary albedo. Using state-of-the-art estimates of /3 one can determine that the direct radiative effect of a 20% change in land area is p r o b a b l y less than that of a 1% change in S. A greater global influence might be the moderation of seasonal climatic e x t r e m e s by the high thermal capacity of the oceans. (Recall that, at present, the annual range of hemispheric m e a n surface air temperature in the northern hemisphere is about 14°C as c o m p a r e d to 6°C for the more oceanic southern hemisphere.) It is probable that a m o d e r a t e d annual cycle of temperature associated with an increase in ocean area would interact with variables which are nonlinear in T (e.g., ice cover, surface albedo, w a t e r v a p o r pressure) to

create changes in the annual mean climate as well. A reduction in glaciation from winters much more m o d e r a t e than t o d a y ' s is a distinct possibility, for example. S o m e w h a t more can be said if one conSiders the zonal distribution of land. A given change in land area at low latitudes, where the incident solar radiation is relatively large, will have a greater influence on the global absorbed radiation than the same change at high latitudes. Thus the distribution of land area with latitude is important for the planetary radiation balance. Polar ice caps could not form easily on continents if there were no land at high latitudes. In this case the s n o w / i c e albedo-temperature feedback would be greatly w e a k e n e d and global climatic stability would increase significantly. The absence of ice at high latitudes would imply a m u c h reduced equator-to-pole t e m p e r a t u r e gradient and probably a less vigorous atmospheric general circulation. Considering the complicated coupling of the general circulation with cloudiness and precipitation, it is difficult even to speculate on the magnitude---or d i r e c t i o n - - o f possible feedbacks. It is not unlikely that an adequate simulation of the climates in the geologic past will need to include the influence of the latitude/longitude distribution of land and the continental and o c e a n - b o t t o m topography. These factors affect the circulation of the a t m o s p h e r e and dominate that of the oceans. Ocean currents, which at some latitudes carry as much or more heat poleward as the a t m o s p h e r e (Oort and V o n d e r Haar, 1976), are constrained by continental coastlines. E v e n a small land bridge can destroy a major circulation. F r o m this point of view the establishment of the Antarctic circumpolar current about 30 million years ago and the subsequent d e v e l o p m e n t of Antarctic glaciation are an intriguing coincidence (NAS, 1975). The continental configuration's influence on the a t m o s p h e r i c circulation is considerably w e a k e r than its influence on the circulation of the oceans. E v e n so, the geographi-

COSMIC CONCLUSIONS, CLIMATIC MODELS cal distributions of topography and surface heat sources create a large stationary eddy c o m p o n e n t in the present climatological wind fields (e.g., Manabe and Terpstra, 1974). Furthermore, surface feedbacks induced by variations in the amplitude or phase of these stationary eddies could alter hemispheric annual temperatures by an amount equivalent to the effect of solar constant changes of several percent (Hartmann and Short, 1979). The climatic history of the geologic past is not known in much detail, but more " r e c e n t " general trends are well documented. Figure 4 from Hays (1977) shows estimates of oceanic bottom water temperatures for the last 100 my. Bottom water temperatures in the late Cretaceous were as much as 15°C higher than the temperatures at present. Since cold polar regions imply cold bottom water formation, it is likely that the poles were warm then relative to their temperatures today. This agrees with other geologic evidence that the Earth was relatively ice-free at that time (Hays, 1977). (Perhaps, as we speculated, this was related to w a r m e r winters from the larger thermal capacity implied by submerged continents?) Assuming that the atmospheric composition 108 years ago was not very different from that of today, and barfing any unsuspected changes in solar output, the large temperature decline in Fig. 4 must be explained by o t h e r - - p r o b a b l y int e r n a l - c l i m a t i c mechanisms (allowing the continental configurations to be part of the

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"internal climatic s y s t e m , " that is). However, a credible quantitative explanation of this massive climatic change has yet to be given, although plausible speculations abound. CONCLUSIONS We have shown that although climatic models can be used to estimate the sensitivity of the climate to external forcings, these estimates can vary by perhaps an order of magnitude for forcings occurring over different time scales. Furthermore, considerable uncertainty remains in the specific estimates for each time scale. For the decadal time scale, we infer from the considerable simulation modeling and seasonal systems experiments that the climate sensitivity parameter, /3, is accurate to within, perhaps, a factor of 2 (i.e., /3 150 _ 100°K). If the upper " l i m i t " is to be believed, and if one assumes that a change in CO2 concentration is a similar external forcing to a change in solar constant, then one major conclusion emerges: Projected atmospheric COz increases from human activities will cause significant climatic change by about the end of this century (e.g., see Williams, 1978). This estimate, however, neglects the potential importance of the transient response of the climate system (see Fig. 9 of T h o m p s o n and Schneider, 1979). But truly cosmic conclusions depend on estimates of long-term climatic sensitivity to very large external forcings, estimates whose range makes the uncertainty in decadal/3 seem small by comparison. For example, we have seen (e.g., Fig. 3) that simulation in climatic models of the ice catastrophe is critically dependent on the parameterization of physical processes whose quantitative character leads to order-of-magnitude uncertainties. And these uncertainties increase as we consider climatic conditions for times further and further back from today. Not only does credible reconstruction of planetary climates b e c o m e more ditficult as we go back in time, but the likelihood increases that changes in atmospheric composition, continental locations, orography, solar irradiance, and even galactic dust (among other

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f a c t o r s ) c o u l d a l t e r c l i m a t i c s e n s i t i v i t y estimates based on t o d a y ' s climatic system and its b o u n d a r y c o n d i t i o n s . A n d at the 109y e a r t i m e s c a l e , p r e c i s e l y that f o r w h i c h C H Z e s t i m a t e s are c o n c e r n e d , th e l a t t e r uncertainties must render present climatic s e n s i t i v i t y e s t i m a t e s as " o r d e r - o f - m a g n i t u d e " - - a t t h e v e r y b e s t! I f o n e e s t i m a t e s t h a t c o n t i n u o u s l y habitable z o n e s e x i s t in the " c l i m a t i c s p a c e " b e t w e e n t h e ice c a t a s t r o p h e a n d t h e runaway greenhouse, both of these predicted b y c l i m a t i c m o d e l s , t h e n o n e s h o u l d also p o i n t o u t the l ar g e r a n g e o f u n c e r t a i n t y i n h e r e n t in t h e s t a t e - o f - t h e - a r t o f s u c h m o d eling. A t a m i n i m u m , t h e e s t i m a t e s g i v e n s h o u l d a t t e m p t to b r a c k e t t h e e x t r e m e values of climatic sensitivity obtained by v a r y i n g m o d e l p a r a m e t e r s o v e r t h e i r plausible limits. N o n e o f this is m e a n t to d i s c o u r a g e further ingenious--or even speculative--use of climatic models on cosmic questions. B u t w e c o n c l u d e that c o s m i c c o n c l u s i o n s f r o m c l i m a t i c m o d e l s s h o u l d be a c c o m p a nied by clear admission of the vast uncert a i n t i e s in the c l i m a t i c c o m p o n e n t o f th e a r g u m e n t , let a l o n e o t h e r p a r t s o f t h e p r o b lem. ACKNOWLEDGMENTS We wish to thank Drs. C. Leovy, S. Warren, R. Cess, and V. Ramanathan for their criticisms of early drafts; C. SaRan for suggesting that we write the article; and H. Howard for typing the manuscript and its revisions. REFERENCES BARRON, E. J., SLOAN, J. L., AND HARRISON, C. G. A. Potential significance of land-sea distribution and surface albedo variations as a climatic forcing factor: 180 m.y. to the present. Palegeography, Paleoclimatology, Paleoecology, in press. BUDYKO, M. I. (1969). The effect of solar radiation variations on the climate of the Earth. Tellus 21, 611-619. CEss, R. D. (1976). Climate change: An appraisal of atmosphere feedback mechanisms employing zonal climatology. J. Atmos. Sci. 33, 1831-1843. CESS, R, D. (1978). Biosphere-albedo feedback and climate modeling. J. Atmos. Sci. 35, 1765-1768. CESS, R. D., ANDRAMANATHAN,V. (1978). Averaging

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