CP-2156 Life In The Universe

 

Cosmic Conclusions from Climatic Models: Can They Be Justified?

STEPHEN H. SCHNEIDER and STARLEY L. THOMPSON

 

 

[127] Sweeping conclusions based on mathematical climatic models should be accompanied by a clear admission of the vast uncertainties in the climatic component of the argument, let alone other parts of the problem.

 

RECENT INTEREST IN CLIMATIC MODELING

 

Climatic modeling is coming of age. What was hardly a defined field only a decade ago (see SMIC, 1971) grew in scope very rapidly during the mid-1970s (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 (GARP, 1979). Moreover, no longer are climatic models built primarily as tools to improve our understanding of climatic phenomena; they are increasingly being asked to shed light on two bolder fundamental questions: (1) What is the impact of human activities on climate? (2) How have climate and life coevolved on Earth? (And a corollary: how might climatic evolution on other planets offer conditions conducive to some forms of life?) Answers to these questions, particularly the Second one, based on climatic modeling could well be termed, as we have, "cosmic conclusions."

How justified are conclusions derived from state-of-the-art climatic models? We will begin to address this question by briefly and selectively reviewing a few of the cosmic conclusions from early modeling efforts. We then turn to a review of the factors whose influences need to be modeled Properly if conclusions from climatic models are to be reasonably credible.

[128] We finish with some cosmic conclusions of our own on the justifications for using state-of-the-art (or likely near future) climatic models to study cosmic issues such as the coevolution of climate and life.

 

Modeling the Sensitivity of Earth's Climate

 

Ice catastrophe- A basic problem that has occupied most climate modelers is simply: what is the sensitivity of Earth's climate to perturbations in boundary conditions external to the atmosphere? These could include changes in the solar "constant" (S), atmospheric composition, the heat input from human activities, the land-sea distribution, orbital elements that govern the geographic and seasonal distribution of incoming solar radiation, or the surface properties of land, ice, or sea.

The simplest calculation we can perform with a model is to find the response, Greek letter beta,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: Greek letter beta

is a very sensitive, nonlinear function of S. Whereas a continuous, but small, decrease in S (less than about 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 icecovered Earth! Furthermore, as noted by North (1975) and Gal-Chen and Schneider (1975), Earth would remain glaciated unless S increased by tens of percent over its present value.

This "ice catastrophe" was the cosmic conclusion that gave the impetus for the dramatic growth during the 1970s in the number of climatic models and modelers. Later on we will digest the findings over the decade since the work of Budyko and Sellers (see, e.g., Thompson and Schneider, 1979, for an updated list of references) 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, like most main-sequence stars, gradually increases in luminosity with time, which would mean that S was some tens of percent less a few billion years ago than it is today. A paradox then arises: how could S have been that low and the Earth have escaped the ice catastrophe? Sagan and Mullen (1972) suggested that the answer might lie in the composition of the primordial atmosphere. Their hypothesis was that the added "greenhouse effect" of more infrared-opaque ammonia in the atmosphere could permit both a lower S and a nonglaciated Earth, even if the Greek letter beta

of the Budyko or Sellers models were accurate. Henderson-Sellers and Meadows (1977) and Owen et al. (1979), for example, recently concurred with the idea that the infrared (JR) opacity of the primordial atmosphere was higher than that of the present atmosphere, but they argue that CO2, rather than ammonia, was the "greenhouse gas."

[129] Regardless of the outcome of the debates over the ice catastrophe results, the faint early Sun paradox, or the primordial atmospheric compost tion, one conclusion clearly emerges: climatic models must consider the nature of the climatic system and its boundary conditions (e.g., atmospheric composition and solar irradiance) for the time at which the model is applied. A model derived from modern conditions may not be applicable to past times when conditions were vastly different.

 

Modeling of Atmospheric and Climatic Evolution

 

A number of authors have recognized that the evolution of the composition of a planet's atmosphere has an important effect on the evolution of its climate. For example, Rasool and de Bergh (1970) investigated relationships among the planet-star distance, the evolution of planetary surface temperature, the IR opacity of the atmosphere, and the feedback effect of these factors on the evolution of atmospheric composition and climate. Hart (1978, 1979) and Zhe-Ming (1978) have made similar calculations. Although each 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. But is it sufficient?

In view of the uncertainty in the time evolution of actual planetary atmospheric compositions (compared to those assumed or computed in the models), there is reason to question specific results. And, perhaps even more importantly, atmospheric composition is not the only factor in the climatic system or its boundary conditions that 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 that attempt to simulate changes on this billion-year time scale (e.g Hart, 1978, 1979). How justified can the results of these pioneering studies be in light of (1) what is known (and unknown) about the properties of our present climate and (2) the likelihood that many of the factors that could contribute to vastly different climatic conditions are not included-or are included improperly-in climatic models?

 

Continuously Habitable Zones

 

Here we will explore in more detail the cosmic conclusions regarding the habitability of Earth for life. One may assume that there is a certain habitable zone around a main-sequence star of a given luminosity (Huang, [130] 1959, 1960). For our purposes, the habitable zone may be defined as that region in which a planet can retain a significant amount of liquid water at its surface, assuming a suitable atmospheric pressure. The climatic extremes that would prevent a habitable Earth are then the cases where all the water has been evaporated from the surface (runaway greenhouse), or where Earth has become completely glaciated (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, extrapolation of CHZ results from Earth models to other stellar systems will be credible only if it can be shown that a significant number of planets that form around main-sequence stars are similar to primitive Earth.

Rasool and de Bergh (1970) concluded that a runaway greenhouse would likely have occurred on Earth had the planet formed closer than about 0.9 AU to the Sun. Hart (1978), using a more physically comprehensive Earth model, estimated that the CHZ around a Sun-type star extends from roughly 0.95 to 1.01 AU. Hart (1979) applied his atmospheric evolution model to other main-sequence stars and found, as a consequence of the ice catastrophe, that no CHZ exists about most K or M stars (the Sun is a G2). Furthermore, stars greater than 1.2 solar masses induced a runaway greenhouse in the model planetary atmosphere. The results of these thought-provoking models are uncertain due to such factors as crude parameterizations, the possible omission of relevant processes, and the lack of good data for early Earth needed to verify the models' results.

In the remainder of this paper we will review results that help to bracket the uncertainties in some basic parameters determining the CHZ- uncertainties that arise from our incomplete knowledge of the climatic component. We begin by discussing Earth's present climatic sensitivity to solar constant changes as estimated from state-of-the-art climatic theory. Theory may be aided somewhat by observations of climatic "systems experiments." But even if the present climatic sensitivity were well determined, problems imposed by the evolution of the surface and atmospheric composition would remain formidable. As an example of a long-term complicating factor, we will discuss some possible climatic consequences of continental drift. We will conclude by suggesting that estimates of the CHZ should, at a minimum, bracket the extreme possibilities resulting from simulations using plausible extreme values of uncertain basic parameters in the models.

 

[131] PRESENT CLIMATIC SENSITIVITY TO EXTERNAL FORCING

 

Radiative Effects

 

In order to determine a CHZ, we must be able to compute the complete time evolution of Earth's surface temperature. A less ambitious, but still relevant, preliminary task is to determine the sensitivity of Earth's present equilibrium climate to changes in the solar constant. As a first approximation, it is possible to consider only radiative effects. The simplest model of equilibrium surface temperature is the radiative balance:

mathematical equation(1)

where FIR is the outgoing terrestrial infrared irradiance, T is the planetary temperature, Greek letter epsilon is a constant effective emissivity, Greek letter sigma is the Stefan-Boltzmann constant, S is the solar constant, and Greek letter alpha subscript p is the planetary albedo. As defined in Schneider and Mass (1975), a global climatic sensitivity parameter is

mathematical equation(2)

where S0 is the present solar constant. From equation (2), for the present Earth case with no internal feedbacks (i.e., Greek letter epsilonandGreek letter alpha subscript p constant), Greek letter beta

is about 70 K (ne., a 1% change in S produces a 0.7 K change in T). If Greek letter epsilon or Greek letter alpha subscript p could change with T, these feedback effects could radically change Greek letter beta

.

A very important positive temperature/radiation feedback results from the increase in atmospheric water vapor with increasing temperature. For the present Earth, this effect makes mathematical symbol more nearly a linear function of the surface temperature than equation (1) would indicate. Figure 1 shows the outgoing terrestrial infrared irradiance as measured by satellite plotted against observed surface temperature. (From here on, T refers to air temperature at the surface.) If we let mathematical symbol

be a linear function of T, mathematical symbol

= A + BT where A and B are constants, the climatic sensitivity is inversely proportional

mathematical equation(3)

(see Appendix of Schneider and Mass, 1975). The water vapor and other feedbacks implicit in the IR observations from satellites yield a B which when used in the climate models of Schneider and Mass (1975) or Cess.....

 


[
132]

Figure 1. Mean monthly values (12 months at 18 latitude zones) of zonally averaged outgoing infrared irradiance , measured by satellites (Ellis and yonder Haar, 1976) plotted against corresponding values of surface air temperature T. The straight line is a least-squares fit to the data. Note that physical processes in the real atmosphere lead to a fairly linear dependence of on surface temperature, as opposed to the T4 relationship of simple theory. (Source: Warren and Schneider, 1979).

Figure 1. Mean monthly values (12 months at 18 latitude zones) of zonally averaged outgoing infrared irradiancemathematical symbol

, measured by satellites (Ellis and yonder Haar, 1976) plotted against corresponding values of surface air temperature T. The straight line is a least-squares fit to the data. Note that physical processes in the real atmosphere lead to a fairly linear dependence of mathematical symbol

on surface temperature, as opposed to the T4 relationship of simple theory. (Source: Warren and Schneider, 1979).

 

.....(1976) or Warren and Schneider (1979), increases Greek letter beta

to about 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 becomes harder to determine. Clouds decrease mathematical symbol

relative to a cloudless sky since their tops usually radiate at a lower temperature than the surface. Ramanathan (1977) found the effect of a given amount of cloud cover mathematical symbol

on to be very nearly a linear function of the temperature difference between the cloudtop and Earth's surface. Thus, in a model calculation , Greek letter beta

can vary by a factor of about 2, depending on the assumptions one makes concerning cloudtop temperature changes, let alone changes in cloud amount.

[133] Except over highly reflective surfaces, clouds will increase the planetary albedo. Furthermore, the albedo of clouds appears significantly with increasing solar zenith angle (Cess, 1976). Figure 2 shows the annual variation of Greek letter alpha subscript p

at several latitudes, as measured by satellite (Ellis and Vonder....

 


Figure 2. Annual variation of Earth's zonally average planetary albedo as observed by satellites (Ellis and Vonder Haar, 1976) and as computed by a model accounting for variations in surface albedo, cloudiness, and solar zenith angle. Cloud albedo is assumed to obey the albedo/zenith- angle relationship suggested by Cess (1976). More than half the annual variation of the computed albedos is due to solar zenith angle changes. Most of the remaining computed variation is a result of surface albedo changes.(Source Thompson, 1979).

Figure 2. Annual variation of Earth's zonally average planetary albedo as observed by satellites (Ellis and Vonder Haar, 1976) and as computed by a model accounting for variations in surface albedo, cloudiness, and solar zenith angle. Cloud albedo is assumed to obey the albedo/zenith- angle relationship suggested by Cess (1976). More than half the annual variation of the computed albedos is due to solar zenith angle changes. Most of the remaining computed variation is a result of surface albedo changes.(Source Thompson, 1979).

 

[134] ....Haar, 1976) and calculated by Thompson (1979) using Cess's albedo/zenith-angle relationship. More than half the annual variation in Greek letter alpha subscript parising 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 controversial. Cess (1976) estimated no net effect, but the observations of Ellis (1978) indicate that the influence on planetary albedo dominates the influence on mathematical symbol

for the present climate. Cess's calculation, however, was for incremental changes in cloud amount away from present values, whereas Ellis's calculation was for a change in cloud amount from zero to total cloud cover. In any case, the uncertainties in basic parameters (such as cloud or surface albedos or cloudtop 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 cloudtop temperature. There appears to be no obvious way to do this at present except to use 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, fc, 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 H2O, is approximately an exponential function of the surface temperature through the Clausius-Clapeyron relationship. The consequence is that fc 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 strong fc(T) dependence is clearly highly debatable. The empirical evidence does not support such a parameterization (Cess,1976); dynamical modeling studies (e.g., Roads, 1978; Schneider et al. 1978; Wetherald and Manabe, 1975) indicate a slight decrease of fc with increasing global temperature. Furthermore, while Hart explicitly includes the effect of fc on the planetary albedo, the influence of cloud amount on mathematical symbol is incorporated only by tuning the infrared parameterization to the present conditions (i.e., mathematical equation = o) This is an extreme assumption in view of the empirical evidence and theoretical reasoning mentioned earlier.

The net result of these parameterizations is the strong negative cloud amount/surface temperature feedback that stabilizes Hart's model, particularly against the ice catastrophe. Indeed, if more plausible assumptions of [135] 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.

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 be a 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 increase with decreasing surface temperature. Thompson (1979) calculates that somewhat less than half the annual variation in Greek letter alpha subscript p

shown in figure 2 is a result of seasonal snow cover and sea ice variations. Cess (1978) has 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 latitudes. This is based on field evidence that deserts were more extensive during ice ages. Simple climatic models may approximate these effects by making Greek letter alpha subscript p

a nonlinear function of the surface temperature.

Figure 3 illustrates the variation in global climatic sensitivity resulting from various choices of the coupling of temperature to mathematical symbol

and Greek letter alpha subscript p

; B is as defined earlier formathematical symbol

, and f is mathematical symbol

(for 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 present value of the solar constant. Two types of climatic sensitivity can be seen. As defined by equation (2), Greek letter beta is approximately proportional to the slope of the curves at the point of no change in S. This is a local stability (more aptly, a local sensitivity) since it is only applicable to small deviations from the present climate The global stability 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 figure 3 were chosen to indicate a plausible range of uncertainty in present theoretical estimates of Greek letter beta

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.

 

Meridional Heat Transport

 

The assumption of radiative balance at all latitudes cannot, of course, be justified in estimating the global climatic sensitivity. Nor can the effects of the atmospheric and oceanic circulations necessarily be averaged out by.....

 


[
136]

Figure 3. 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.

Figure 3. 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, mathematical symbol

= A + BT (see fig. 1). f is the albedo-temperature coefficient for Sellers' (1969) planetary albedo parameterization. (Of the two values given, f = 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 f) 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).

 

....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 [137] equations for up to several simulated years, integration beyond 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 yonder Haar (1976) for a discussion of 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, 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 summer provides evidence that it does exist. It is not impossible, however, to imagine situations in which circulations could 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, and so forth.

With regard to present climatic sensitivity, the effect of poleward heat transports is to reduce Greek letter beta by decreasing the extent of polar ice. The effect of transports on global stability is less clear. There is a possibility that the circulations may have a strong nonlinear influence on the extent of permanent ice. The plot of ice line vs 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, under 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 in figure 3 (i.e., 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 figure 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 Functions

 

[138] Earlier we discussed one way to estimate the climatic sensitivity parameter , namely, simulation with models based on assumed (or semiempirical) values of the parameters that determine the strength of the climatic feedback processes (which, in turn, determine Greek letter beta

). The integral effect of all such feedback processes still cannot be verified, given the uncertainties in current climatic models and in the supporting observational data (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 us to search for an empirical method of checking model estimates of Greek letter beta

, 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 "experiments" can, by analogy to systems analysis, help to identify a transfer function" that will characterize the climatic system more adequately than do present theory and observation. (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 that control climate sensitivity (e.g.,Greek letter alpha subscript p

or mathematical symbol

) to reproduce in a model the observed climatic response to a known forcing. For a zonal energy balance model, we have

mathematical equation(4)

where div F represents net heat transport out of latitude zoneGreek letter phi, and R is the thermal inertia of each zone (Thompson and Schneider, 1979). In this example Q(Greek letter phi, t) represents the seasonal solar forcing and mathematical symbolthe seasonal temperature response (both of which are well known). The transfer function is made up of the parameters that relate the terms in each of the square brackets m equation (4) to the dependent (T) and independent (Greek letter phi,t) variables. But there are at least three separate feedback terms in the square brackets and, moreover, R must be specified or calculated, so that one probably could reproduce the responsemathematical symbol, to a known forcing, Q(Greek letter phi, t), with a nonunique set of plausible parameterizations comprising the transfer function. Systems experiments are thus of limited usefulness in deriving or verifying individual parameterizations that determine a model's sensitivity. Systems experiments [139] can be important for verifying the overall climatic sensitivity of models to a given external perturbation. Unless parameterizations are individually validated, however, a 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.

 

Examples of Systems Experiments

 

Seasonal cycle- We have already mentioned that the seasonal cycle is an excellent example of a clear external forcing and a statistically significant climatic response. For example, it is known that the range 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 (North and Coakley, 1979; Thompson and Schneider, 1979)- that the larger ratio of water to land in the SH relative to the NH leads to a larger value of thermal inertia in the SH relative to the NH. This larger R results in greater seasonal heat storage and a smaller seasonal temperature cycle amplitude. In this example, 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 commutations of compensating errors in estimates of transfer-function parameterizations, are also possible.

What is needed then is enough independent observational data to fix parameterizations for the terms in square brackets in equation (4) with fairly narrow ranges of uncertainty. Also, data for parameters like R are needed as well. Data such as those plotted on figures 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 climatic sensitivity of models.

Volcanic dust veils- It has long been suspected that the stratospheric dust veils that follow explosive volcanic eruptions affect climate by interfering with radiative transfer between Earth and space (see Mass and Schneider, 1977, for references). The existence of a potential volcanic signal in long-term climatic statistics has remained controversial because 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 that a cooling of a few tenths of a degree Celsius can be detected in a few dozen long-term temperature records (Mass and Schneider, 1977). However, because of the weak [140] signal/noise 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 in which the radiation perturbations are well documented are needed before the observed climatic response can be usefully compared to global climate model calculations.

Orbital element 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 quarternary glaciations is commonly known as the "Milankovitch hypothesis." Spectral analyses of the time series of oxygen isotope ratios in two ocean sediment cores (Hays et al., 1976) 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 attempts to model physically possible connections between the insolation perturbations and the hypothesized glacial/ interglacial response. This Milankovitch climatic change experiment has been performed with a variety of energy balance models (Suarez and Held, 1976; North and Coakley,1979; Schneider and Thompson, 1979). In all cases similar results were obtained. The simulated temperature record in the NH led the observed record by some 5000 years, and the amplitude of simulated glacial/interglacial transitions was considerably less than the observed amplitude. The modelers have all speculated that the phase error could 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 NH 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 between 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 an underestimate of about a factor of 2 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 that performs well in a seasonal simulation cannot necessarily be trusted to reliably estimate climatic sensitivity 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 [141] albedo, orography, or evapotranspiration are considered, it is quite possible (perhaps likely) that a Greek letter beta

that 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 from a Greek letter beta

for forcings occurring over millennia. If even longer time scales are considered, then interactions among atmosphere, oceans, ice, and lithosphere could readjust the sensitivity estimates once again (Sergin and Sergin, 1976).

Climatic modeling is only beginning to assess quantitatively the potential importance of processes occurring over different 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 considering changes in surface conditions or atmospheric composition on geological time scales (greater or equal to107 yr). It is now accepted that continental shapes and locations have changed over geologic time. As one example of a long-term complicating factor, we will discuss some possible climatic effects of changes in continental configuration.

The grossest measure of land-sea distribution is the fractional area of the globe covered by land. This quantity has varied by 20% in the past 180 million years (Barron et al., 1980). 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 Greek letter beta

, one can determine that the direct radiative effect of a 20% change in land area is probably less than that of a 1 % change in S.

A greater global influence might be the moderation of seasonal climatic extremes by the high thermal capacity of the oceans. (Recall that, at present, the range of hemispheric mean annual surface air temperature in the NH is about 14°C compared to 6°C for the more oceanic SH.) It is probably that a moderated annual cycle of temperature associated with an increase in ocean area would interact with variables nonlinear in T (e.g., ice cover, surface albedo, water vapor pressure) to create changes in the annual mean climate as well. A reduction in glaciation from much more moderate winters than today is a distinct possibility, for example.

We can say more if we consider 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 icecaps [142] could not form easily on continents if there were no land at high latitudes. In this case the snow/ice albedo-temperature feedback would be greatly weakened and global climatic stability would increase significantly. The absence of ice at high latitudes would imply a much reduced equator-to-pole temperature gradient and probably 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 direction, of 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 ocean-bottom topography. These factors affect the circulation of the atmosphere and dominate that of the oceans. Ocean currents, which at some latitudes carry as much or more heat poleward as the atmosphere (Oort and yonder Haar, 1976), are constrained by continental coastlines. Even a small land bridge can destroy a major circulation. From this point of view the establishment of the Antarctic circumpolar current about 30 million years ago and the subsequent development of Antarctic glaciation is an intriguing coincidence (NAS,1975).

The continental configuration does not have as rigid an influence on the circulation of the atmosphere as it does on that of the oceans. Even so, the geographical distributions of topography and surface heat sources create a large stationary eddy component in the present climatological wind fields (Manatee 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 "recent" general trends are well documented. Figure 4 shows estimates of oceanic bottom water temperatures for the last 110 million years. Bottom water temperatures in the late Cretaceous were as much as 15°C warmer than at present. Since cold polar regions imply cold bottom water formation, it is likely that the poles were warm relative to today. This agrees with other geologic evidence that Earth was relatively icefree at that time (Hays, 1977). (Perhaps, as we speculated, this was related to warmer winters from the larger thermal capacity implied by submerged continents?) Assuming that the atmospheric composition 100 million years ago was not very different from today, and barring any unsuspected changes in solar output, the large temperature decline in figure 4 must be explained by other, probably internal, climatic mechanisms (i.e., allowing the continental configurations to be part of the "internal climatic system"). A credible quantitative explanation of this massive climatic change has yet to be given, although plausible speculations abound.

 


[
143]

Figure 4. Bottom water temperatures during the last 108 years as estimated from the oxygen isotope ratio 18O/16O of the fossil shells of benthic foraminifera (after Hays, 1977).

Figure 4. Bottom water temperatures during the last 108 years as estimated from the oxygen isotope ratio 18O/16O of the fossil shells of benthic foraminifera (after Hays, 1977).

 

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, Greek letter beta

, is accurate to within, perhaps, a factor of 2 (i.e., Greek letter beta

is equivalent to150 ±100 K). If the upper limit is to be believed, and if one assumes that a change in CO2 concentration is a similar external forcing to change in solar constant, then one major conclusion emerges: projected atmospheric CO2 increases from human activities will cause significant climatic change by the end of this century (see Williams, 1978).

Truly cosmic conclusions depend on estimates of long-term climatic sensitivity to very large external forcings, estimates whose range makes the uncertainty in decadal Greek letter beta

seem small by comparison. For example, we have seen that simulation in climatic models of the ice catastrophe critical!) depends on the parameterization of physical processes whose quantitative character leads to order-of-magnitude uncertainties. And these uncertainties [144] increase as we consider climatic conditions for times further and further back from today. Not only does credible reconstruction of planetary climates become more difficult 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 factors) could alter climatic sensitivity estimates based on today's climatic system and its boundary conditions. And at the billion-year time scale, precisely that needed for CHZ estimates, the latter uncertainties must render present climatic sensitivity estimates as "order-of-magnitude" at the very best!

If one estimates that continuously habitable zones exist in the "climatic space" between the ice catastrophe and the runaway greenhouse, both of these predicted by climatic models, then one should also point out the large range of uncertainty inherent in the present state of such modeling. At a minimum, the estimates given should attempt to bracket the extreme values of climatic sensitivity obtained by varying model parameters over their plausible limits.

None of this is meant to discourage further ingenious, or even speculative, use of climatic models on cosmic questions. But we conclude that cosmic conclusions from climatic models should be accompanied by clear admission of the vast uncertainties in the climatic component of the argument, let alone the other parts of the problem.

 

Acknowledgments

 

We thank Dr. C. Leovy, S. Warren, R. Cess, and V. Ramanathan for their criticisms of early drafts; C. Sagan for suggesting that we write the Icarus version (Schneider and Thompson, 1980); and H. Howard for typing the draft manuscript and its revisions.

 

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