SCOPE 29 - The Greenhouse Effect, Climatic Change, and Ecosystem

5.1 INTRODUCTION

Climate is popularly thought of as some sort of average weather and its fluctuations. More precisely, climate statistics are obtained by averaging weather over a period long compared to the deterministic limit of predictability for atmospheric motions, which is about two weeks. The climate system is now recognized to also include the oceans, ice sheets, and land-surface properties (Houghton, 1984) because of the close interactions between these and the atmosphere. Climate can vary from year to year, fluctuate on time scales of several years, or change on longer time scales. Detecting the effects of warming by CO₂ and other trace gases requires establishing the occurrence of long-term change that is statistically significant compared to past climate normals. Climate statistics can be obtained by averaging data over a large number of years, e.g., 30 years of data are usually used to define 'normals'. However, since climate is always changing, there are no fixed normals so that the statistics will always depend on the averaging period.

A more rigorous definition of climate is obtained by using, rather than a time average, an ensemble average, that is, the average over a hypothetical infinite set of Earths with the same external influences (i.e., the same solar input, the same atmospheric composition, etc.) but different detailed weather patterns.

This ensemble average idea introduces two new concepts, those of weather noise and of external influences. Weather noise is the uncertainty in the ensemble average arising from the sampling of unpredictable weather fluctuations, namely that part of climatic variability which arises from day-to-day weather variations. This noise is always present in a climate statistic. The term external influences implies that the climate can be affected either by external or by internal factors. What constitutes an external influence depends, in practice, on the time scale of interest. For example, the input of energy from the Sun will always be an external factor, but the extent and pattern of ice and snow cover (which help to determine how much solar radiation is reflected away from the Earth's surface) could be considered an external factor on short time scales, but an internal factor on long time scales. 

5.2 CAUSES OF CLIMATIC CHANGE

External changes in global climate are forced by various processes that change the flows of radiative energy within the system. Either the absorption of solar radiation or the trapping of longwave radiation by atmospheric constituents may change.

Possible reasons for change include:

1. A change in solar output (irradiance) or a change in the geometry of the Earth's orbit around the Sun.
2. A change in the fraction of incoming (shortwave) energy at the top of the atmosphere which is absorbed by the surface or atmosphere.
3. A change in the amount of net outgoing (longwave) energy at the top of the troposphere.
4. A change in the amount of heat sequestered by the deep ocean. 

The primary changes under headings (2) and (3) may result from: 

1. Changes in the fluxes of radiation caused by changing atmospheric composition.
2. Changes in atmospheric transmissivity resulting from either variations in the amount of volcanic or anthropogenic aerosol in the atmosphere, or variations in cloudiness.
3. Changes in the amount of radiation reflected by the Earth's surface (albedo changes).
4. Changes in the amount of longwave radiation emitted by the surface and/or absorbed by H₂O in the atmosphere.

Solar output is known to vary on very long time scales (see, for example, Newkirk, 1983) and to vary markedly in the ultraviolet and higher frequency parts of the spectrum on short time scales (days to years) (Foukal, 1980). Variations in solar irradiance of ±0.1% occur with the 27-day equatorial solar rotation period (Smith et al., 1983). There is, however, only indirect evidence for variations of climatological significance on time scales from 1 to 2,000 years. The influence of sunspots on climate is uncertain, but very few convincing statistical relationships have been demonstrated (Pittock, 1978, 1983), and any effects are likely to be small. Correlations between solar irradiance and sunspots have been demonstrated (Willson et al., 1981; Eddy et al., 1982; Smith et al., 1983) and irradiance changes of 0.05% over an 11-year sunspot cycle are implied by analyses of short periods of satellite data. However, these solar-cycle related fluctuations could only have minor effects on global mean temperature, almost certainly below the limit of detectability.

Satellite data on solar variability also show a secular trend (amounting to 0.1% when extrapolated to a 40-year period) that may be more important. Since solar output should vary as the diameter of the Sun varies, and since there is astronomical evidence that the solar diameter varies on the 10- to 100-year time scale, we might expect solar irradiance to vary on these time scales. For example, there appears to be an approximately 80-year cycle in the diameter of the solar disc (Parkinson et al., 1980; Gilliland, 1980, 1981) implying a similar cycle in irradiance. However, the theoretical diameter-output relationship has considerable uncertainty, up to 2 orders of magnitude (Gilliland, 1982). If the secular irradiance trend observed in satellite data is related to diameter changes, as Smith et al. (1983) have suggested, then the amplitude of the suggested 80-year cycle in solar irradiance would be about 0.1 %, enough to cause a global mean temperature cycle of around 0.1 °C amplitude.

The satellite record of solar irradiance spans only a few years and it is not yet known how representative these data are of longer time scale variations. Some ground-based observations of solar features do, however, show marked variations on the decadal to century time scale. The analysis of accurately dated tree rings shows that the atmospheric concentration of the radioactive isotope carbon-14 has varied significantly in the past on these time scales. Since C-14 concentration is determined by its production rate in the stratosphere, which in turn is influenced by solar flare activity and the strength of the solar wind (Stuiver and Quay, 1980), we know that these solar parameters vary on the 10- to 100-year time scale. A statistically significant 200-year periodicity has been shown to exist in the atmospheric C-14 record over the past 8,500 years (Sonett, 1984). However, there is as yet no firm evidence that these C-14 fluctuations correlate with fluctuations in climate (Stuiver, 1980; Williams et al., 1980).

Orbital Variations

Changes in the Earth's orbit around the Sun affect climate on time scales of 1,000 years or more by changing the latitudinal and seasonal distribution of incoming solar radiation at the top of the atmosphere. Locally, these changes can be 10% or more (Berger, 1979). North et al. (1983) have reviewed past modelling work and have suggested that with the present configuration of the land masses in the Northern Hemisphere a nonlinear ice-albedo feedback may enhance the development of large ice masses when the orbital elements are such that they favour cool Northern Hemisphere summers.

Orbital variations also affect the latitudinal and seasonal distribution of incoming solar radiation slightly on much shorter time scales (Borisenkov et al., 1983).

 Volcanoes

 Volcanic eruptions inject into the stratosphere both dust and sulphur compounds which are converted to secondary aerosols. The latter is currently thought to be of more radiative importance (Rampino and Self, 1984). Individual volcanic eruptions may cause cooling up to around 0.3 °C in global mean surface air temperature by their screening effect on solar radiation (e.g., Hansen et al., 1978; Newell and Deepak, 1982) and warming by several degrees in the absorbing layers in the stratosphere. Observational data show surface cooling on the monthly to annual time scale (e.g., Lamb, 1970; Oliver, 1976; Taylor et al., 1980; Self et al., 1981; Mitchell, 1983; Kelly and Sear, 1984), but in the tropical troposphere volcanic effects cannot be convincingly demonstrated, possibly because they are obscured by variability associated with the El Niño/Southern Oscillation phenomenon (Parker, 1985). Stratospheric data, however, offer convincing support of model predictions (e.g., Parker and Brownscombe, 1983; Labitzke et al., 1983; Quiroz, 1983).

The effects of volcanic eruptions on past climate are difficult to assess because the observational record can be interpreted in alternative ways, and, equally importantly, because the volcanic forcing record is not well documented. At least four distinct types of volcanic records exist: the historical 'Dust Veil Index' of Lamb (1970) and others (e.g., Hirschboeck, 1980); the geological record of Simkin et al. (1981) (see also Newhall and Self, 1982); time series of atmospheric transmissivity (e.g., Pivovarova, 1977; Bryson and Goodman, 1980); and the Greenland ice core acidity record (Hammer, 1977; Hammer et al., 1980). These different records show broad similarities, but also significant differences. The uncertainty in the volcanic forcing record has been highlighted by recent direct measurements of stratospheric sulphate aerosol concentration covering the period 1971-1981. These revealed a number of volcanic injection events that had not previously been reported (Sedlacek et al., 1983).

Many atmospheric trace gases are radiatively active; they absorb and reradiate energy at both long and short wavelengths. The most important such gases are H₂O, O₃, CO₂, N₂O, CH₄ and chlorofluoromethanes (CFMs).

Water vapour is an internal factor (whose concentration varies widely in space and time) while CFMs, being of strictly anthropogenic origin, are purely external. Other trace gases, such as O₃, CO₂, N₂O, and CH₄, have concentrations which are influenced by the activities of Man, but may also vary naturally as parts of the internal feedbacks of the climate system as a whole.

Changes in the concentrations of any of these gases affect the way incoming and outgoing energy is distributed in the vertical, and increases may cause significant warming of the troposphere and cooling of the stratosphere.

The concentrations of several of these radiatively active gases are increasing within the atmosphere, and their concentrations can be projected into the future empirically or through modelling their sources (see Chapter 4). Of these gases, the increase of carbon dioxide (CO₂) is the most important from the viewpoint of its projected climate effect. It is also the best understood as a result of a relatively long data record for its concentration (since 1958) and relatively good accounting for its past sources, as reviewed in detail in Chapters 2 and 3 of this report.

Other trace gaseous atmospheric constituents are also of concern because their increases add to the CO₂ climate warming (World Meteorological Organization, 1982). Of particular importance are increases of the chlorofluorocarbons F-11 and F-12, nitrous oxide, methane, and ozone, listed in order of increasing ignorance as to the sources causing their increase and decreasing length of the data record. Ramanathan et al. (1985) have recently reviewed the questions of atmospheric trace gas concentrations and climate effects. See also Chapter 4.

The radiative effects of changes in atmospheric aerosol content due to human activities have been speculated on for many years but cannot yet be quantified (cf World Climate Research Programme, 1983, for a recent review of this subject; and Cess, 1983, for the question of Arctic aerosols). Possible climate effects of future land-use changes are another difficult topic that will not be treated in this review (cf Dickinson, 1981a; Henderson-Sellers and Gornitz, 1984, for treatments of the global effects of land-use change). Land-use changes are primarily of interest to global average climate because of their connections to the carbon cycle.

Internal causes of climatic change, e.g., as a result of changes in ocean temperatures and circulation, cloudiness, or sea-ice cover should be modelled as part of the internal climate system as discussed in later sections. However, we cannot exclude possible long-term natural trends in these parameters that would most usefully be regarded as external changes.

5.3 INTRODUCTION TO MODELLING THE CLIMATE SYSTEM

Models to better understand future climate resulting from changing atmospheric composition have been developed over the last two decades. The first component of any such model is the determination of the changes in atmospheric radiative fluxes which would result from the changed atmospheric composition. This determination requires good models for the transfer of atmospheric radiation through the relevant trace gases. The subject of atmospheric longwave radiation is complicated by the need to consider the tens of thousands of spectral absorption lines of the trace gases and their overlap with major absorbers, especially water vapour. However, such calculations can be done reasonably accurately for CO₂ and adequately for the other trace gases. Errors in radiative calculations introduce a relatively small (although not negligible) uncertainty into estimates of future climatic change and need not be reviewed further here (cf Dickinson, 1982; World Meteorological Organization, 1982; Kiehl and Ramanathan, 1983; Ramanathan et al., 1985, for more detailed discussion of the uncertainties in the calculation of trace gas radiative effects).

Recent reviews of the question of modelling the climate effects of increasing CO₂ have been given by Dickinson (1982), CO₂/Climate Review Board (1982), Schlesinger (1983a, b), and Gilchrist (1983). More general recent treatments of the CO₂ problem include Carbon Dioxide Assessment Committee (1983), Jäger (1983), and Seidel and Keyes (1983).

5.4 TYPES OF MODELS-THEIR FEEDBACKS

5.4.1 Reasons for Different Models

The climate system involves transfers of energy between a three-dimensional turbulent and radiatively active atmosphere and spatially heterogeneous land, ocean, and cryosphere surfaces. This system is very complex and it has not yet been possible to produce models that use 'state-of-the-art' descriptions of either the atmospheric or surface processes. Furthermore, our 'state-of-the-art' understanding of some processes is still not satisfactory, as later discussed. Thus, various approximations and simplifications have been made to develop climate models, some based on empiricism. Because of lack of consensus as to which approximations do least damage to modelling results, many different modelling approaches have been developed. Some of these approaches have been superseded by more elaborate models that treat all physical processes essentially as well or better than they are treated in the simple models. The simple models still remain of interest because their relative computational economy allows consideration of a much wider range of parameter values. Furthermore, the simpler models can usefully provide insight and description of the dominant processes in the more elaborate models. That is, they are diagnostic and educational. 

5.4.2 Zero-dimensional Model

One procedure used for simplification is spatial averaging. Averaging in all dimensions gives the simplest climate model of interest which can be written

where T is the departure of the global average surface temperature from some climatological value, t is time, Q is a perturbation in the net vertical flux of radiation at the tropopause that would take place due to some external change, such as increased CO₂, and in the absence of climatic change. Examples of Q for CO₂ and other trace gases are given in Table 5.1. The term T approximates the change of outward radiative energy flux, evaluated at the tropopause, resulting from global temperature change. The factor has units of Watts meter^-2 °C^-1 and is referred to as the feedback parameter, whereas C is the system heat capacity.

Table 5.l Estimates of Q, the net heating of the troposphere system, for various hypothetical external changes of atmospheric constituents (based on World Meterorological Organization, 1982)

Equation (5.1) has no independent predictive value since and C are best obtained from more detailed models. For example, C depends on the depth to which thermal disturbances penetrate into the ocean which, in turn, depends on the time scale of the heating. Equation (5.1) is also of limited practical use because it only describes global average temperature change. More detailed models provide changes in surface temperature and hydrological processes which differ between locations and thus would be more useful to decision-makers.

 However, Eq. (5.1) warrants attention for several reasons. First, it is straightforward enough that any reader with a modest calculus background can understand its physical description. In particular, the steady-state warming from increased CO₂ is simply given by Q/, and t_c = C/ defines a time scale required to approach steady state. Second, Eq. (5.1) is very convenient for interpreting the result of more detailed and complex models (as done by Climate Research Board, 1979), a task we shall return to later. Third, through use of Eq. (5.1) to summarize the results of more elaborate models, we can develop some idea as to the likely range of possible future climatic change implied by scenarios for future atmospheric concentrations of carbon dioxide.

 5.4.3 One-dimensional Models

Two further popular general classes of simple climate models are the onedimensional energy balance models (e.g., North et al., 1981) and the radiative convective models (e.g. Ramanathan and Coakley, 1978). These models can be viewed as elaborations of Eq. (5.1) where, for the energy-balance models, T in Eq. (5.1) becomes a function of latitude and in the radiative convective models a function of altitude. With either spatial dimension considered, it is necessary to add to Eq. (5.1) terms for the spatial coupling of temperature by energy transports.

 5.4.4 Energy Balance Climate Models

 Energy balance climate models are solved for temperature as a function of latitude or cosine of latitude, denoted y. The temperature feedback term, A in Eq. (5.1), represents the variation with temperature of outgoing longwave radiation and reflected solar radiation. The longwave component _LW is most simply approximated by a constant term _LW = B, inferred from radiation models (Budyko, 1969) or from the empirical correlation of variations of longwave radiation at the top of the atmosphere observed by satellite with surface temperature (e.g., Cess, 1976). More elaborate treatments also consider the possible dependence of on other parameters, such as temperature, variations in cloudiness, variations in atmospheric water vapour, surface elevation, and changes in atmospheric lapse rate. Estimates of _Lw have varied from between about 1.4 W m^{-2 °}C^-1 and 2.4 W m^{-2 °}C^-1. The ice-albedo contribution is discussed separately below after consideration of transport.

 The atmosphere does not locally reach a balance between radiation fluxes and vertical convection. Rather, it is heated in low latitudes and cooled in high latitudes by net radiative fluxes, i.e., the difference between absorbed solar and outgoing longwave radiation. This gradient in energy deposition provides the heat engine system that drives atmospheric winds and oceanic currents. The atmosphere transports thermal energy in sensible and latent form from warm to cold regions. The oceans may transport about as much thermal energy as the atmosphere. These transport processes are approximated in the energy balance models in various ways. The two simplest approaches are (l) to assume that energy divergence by transport is proportional to ((y)-T), where is global average temperature (Budyko, 1969); (2) to make a diffusion approximation, i.e., transport is proportional to the negative gradient of T, -KT/y, where K is a diffusion coefficient. The convergence of energy by transport is then given by /y(KT/y). With solution by a low-order Legendre polynomial expansion (North, 1975), these two forms of transport are equivalent. More detailed treatments attempt to separate atmospheric and oceanic components of the climate system and make latent heat transport depend on the saturation vapour pressure of water. 

The most realistic treatment of atmospheric transport is to solve explicitly dynamic equations of the time-varying atmospheric winds and use these to transport sensible and latent heat; that is the General Circulation Model (GCM) approach, to which we return later. Some intermediate models (e.g., Chou et al., 1982) consider a separate atmospheric temperature with vertical transports determined as in the radiative convective models to be discussed later.

5.4.5 Ice-Albedo Feedback 

Much of the solar radiation incident on the top of the atmosphere is absorbed at the Earth's surface (about half on a global average). The albedo at the Earth's surface thus is of major importance in determining the actual amount of absorbed solar radiation. Albedo can vary from as low as 0.02 for a clear calm water surface and overhead Sun to greater than 0.95 for fresh snow and visible wavelengths. In general, snow and ice surfaces, if exposed to solar radiation, have much higher albedos than do most land surfaces and liquid ocean under all conditions. Snow and ice can only be present for any length of time at temperatures which are freezing or below. In regions at the margins of ice or snow cover, decreases in surface temperature allow a larger area to be covered by ice and snow. Thus, the amount of absorbed solar radiation decreases with decrease in temperature. This temperature dependence of reflected solar radiation is referred to as ice-albedo feedback. In simple energy balance models, it is included by making albedo a function of temperature, e.g., by assuming a discontinuous increase in albedo where temperatures fall below some critical value (Budyko, 1969; Held and Suarez, 1974) or by making albedo negatively proportional to local temperature with some lower and upper limit representing zero and complete cover by ice and snow (Sellers, 1969).

The basic difference between one-dimensional energy balance models and Eq. (5.1) is the possibility of changes in the latitudinal variation of temperature in the former. If latitudinal temperature gradients are fixed or vary in a manner depending only on global average temperature, the one-dimensional model can be reduced to Eq. (5.1) (e.g., Wang and Stone, 1980). More generally, as already discussed, Eq. (5.l) can be used to interpret more detailed models. In particular, for any model we can always evaluate the ratio of change of global energy reflected by ice and snow to change of global average surface temperature and refer to this as ice-albedo feedback _A. This quantity is generally negative implying a destabilizing or positive feedback. For seasonally varying models, it is only meaningful to define ice-albedo feedback on an annual mean basis. The seasonal variation of albedo can become uncorrelated with seasonal variation of temperature if the albedo variation lags temperature by a season (Mokhov, 1981). Furthermore, while maximum changes in reflected radiation occur in the spring and summer seasons, maximum surface air temperature changes over sea ice are likely to occur in the autumn and winter as a consequence of changes in heat storage and release in the ocean (Manabe and Stouffer, 1980). This thermal inertial effect can swamp the explicit ice-albedo feedback over the seasonal cycle and may considerably amplify the annual average effective ice-albedo feedback (Robock, 1983a).

On longer time scales, additional feedbacks related to changes in continental ice sheets or atmospheric composition may become important. Feedbacks appropriate to past ice ages have been discussed by Hartmann and Short (1979), Held (1982), Bowman (1982), and Oerlemanns (1982).

5.4.6 Radiative-Convective Models 

Radiative-convective models emphasize the effects of variation of temperature with altitude z and allow analysis of stratospheric radiative feedbacks on tropospheric temperatures. The simplest one-dimensional ones consider globally averaged atmospheric temperature T(z). In the stratosphere, T(z) is essentially in radiative equilibrium (e.g., as demonstrated by Fels et al., 1980) and hence determined by a local balance between solar heating and net longwave cooling. The solar heating depends mostly on ozone concentrations. Above the lowest layers in the stratosphere, the longwave cooling is largely controlled by carbon dioxide and is primarily dependent on local temperature. Radiative balance just above the tropopause is complicated by the importance of absorption of longwave radiation originating from warmer tropospheric layers and from the Earth's surface. Not only carbon dioxide but also ozone and water vapour make important contributions to the opacity of the lower stratosphere. Radiative fluxes within and leaving the troposphere depend on the temperature profile, distribution of gaseous absorbers, especially water vapour and CO₂, and on the assumed distribution of cloud properties.

In the troposphere, the vertical variation of T is determined primarily not by local radiative balance but rather by the vertical energy redistribution by moist convective processes. Thus, one element of a radiativeconvective model is a parameterization for tropospheric convection. The classical study by Manabe and Wetherald (1967) introduced the assumption that, if the lapse rate exceeds the 'critical rate' of 6.5 °C/km, a convective adjustment would ensue and maintain the 6.5 ^°C/km lapse rate. Many more recent radiative convective models have used this critical lapse rate. Other alternatives are to use the observed global average lapse rate or to use the lapse rate defined by the moist ascent of a saturated parcel (the moistadiabatic lapse rate) (Rowntree and Walker, 1978; Ramanathan and Coakley, 1978; Lindzen et al., 1982).

The moistadiabatic assumption illustrates the possibility of lapse rate feedbacks (Schneider and Dickinson, 1974; Ramanathan and Coakley, 1978). If a temperature change at the surface is extended upward along a moist adiabat, the magnitude of the change increases with increasing altitude. Outgoing longwave fluxes largely originate within a tropospheric column with only about 0.3 of the total flux coming from surface or near-surface emission in the 8-12 µm window region. Thus, an increase of temperature change with increased altitude amplifies the consequent change of outgoing longwave flux. Thus, a smaller surface temperature change is required to balance a given external change in atmospheric composition or heat input. This process is a negative lapse rate feedback. Hence, models with moist adiabatic adjustment but fixed cloud properties have larger (cf Eq. (5.1)). In GCMs, a process of moist adiabatic adjustment controls to a large extent their tropical temperature profiles.

Alternatively, if a model is heated by large amounts at high elevations (e.g., as argued by Turco et al., 1983, to be the consequence of nuclear war aerosol), then the lapse rate becomes less than the critical value, and moist adjustment no longer couples surface temperature to the tropospheric column. Under these conditions, large temperature changes can occur at the surface in response to changed surface heating with only small additional changes occurring at higher levels in the troposphere. In this case, a much larger surface temperature change would be required to balance some prescribed external change that warms the surface. The lapse rate feedback is positive. Positive lapse rate feedback applies especially to high latitudes for CO₂ warming (e.g., Manabe and Wetherald, 1975; Ramanathan, 1977).

Another important question which needs treatment in radiative-convective models is the amount of water vapour contained by the atmosphere. Manabe and Wetherald examined two assumptions. First, they considered fixed concentrations of water vapour. The temperature change they then inferred corresponds to = 3.7 W m^-2 °C^-1, which would be the feedback for blackbody radiation from a planet with no atmosphere and albedo of 0.30, the presently observed value. Alternatively, they argued that a much more realistic assumption in the presence of climatic change is fixed relative humidity for which they found = 2.2 W m^{-2 °}C^-1. The difference between these two values of 1.5 W m^-2 K^-1 is the positive water vapour feedback of their fixed relative humidity model. Increased water vapour increases the atmospheric trapping of longwave radiation and, to a much lesser extent, absorbed solar radiation, as does increased CO₂. For the actual warming, it is unlikely that relative humidity will stay strictly constant or change in the same way at all altitudes. For this reason and because of the three-dimensional variations of actual water vapour concentrations, changes in relative humidity would also be of considerable importance for determining cloud changes, the subject we turn to next.

5.4.7 Cloud-radiation Feedbacks 

It is evident that the presence of clouds increases the longwave opacity of the atmosphere and hence intensifies the lapse rate feedbacks just discussed for a given temperature profile variation. One of the most important contributions of radiative-convective models has been to clarify other possible feedbacks between cloud cover and atmospheric radiation. Clouds can change in thickness, fractional cover, or in the altitude of their tops, as climate changes. Other more subtle changes such as in the size of cloud droplets or in the cloud horizontal scale may also significantly modify cloud radiative properties.

Manabe and Wetherald (1967) fixed the above cloud properties and obtained, as previously mentioned, a feedback = 2.2 W m^{-2 °}C^-1.Alternatively, some models have assumed fixed cloud-top temperatures. This assumption provides a positive feedback since the longwave flux from the cloud tops cannot then change significantly and the fluxes from the surface, hence surface temperature, must change more. Typically, the assumption of fixed cloud-top temperature reduces by about 0.5 W m^{-2 °}C^-1 from its value for fixed cloud-top altitude. More generally, if cloud altitudes increase with a warmer temperature, the cloud feedback on surface temperature is positive, or vice versa if cloud altitudes decrease. Cloud feedbacks in energy balance models have been discussed by Golitsyn and Mokhov (1978).

The average fraction of the sky covered by clouds may also change with climatic change. Cloud fractional coverage is probably only weakly linked to global or perhaps even local surface temperatures and depends primarily on local atmospheric dynamical processes (e.g., Schneider et al., 1978). For 'average' clouds, changing clouds by the same relative amount at all levels has about twice as large an effect on the amount of reflected solar radiation as it has on the trapping of longwave fluxes. Hence, decreased cloud fraction usually implies increased heating of the climate system. The exception is thin high cirrus clouds, which modulate longwave radiation to a greater extent than solar fluxes.

An increase in the thickness of clouds as described by cloud liquid water content would generally increase the albedo of the clouds but have little effect on the longwave emission of all but nonblack cirrus clouds. Greatest albedo change for given increase in liquid water is possible for relatively thin clouds since thick clouds are essentially saturated in brightness.

Various suggestions have been offered as to how clouds might change with a warmer climate. A warmer atmosphere would hold more water vapour and possibly also more liquid water, hence cloud thickness could well increase. A warmer climate would also probably provide a larger fraction of convective rainfall. Convective clouds tend to concentrate liquid water into small regions with a large amount of clear sky between clouds, as opposed to layer clouds which can uniformly cover a large area. Thus, more convective clouds would probably mean less low cloudiness. On the other hand, convective clouds can have relatively high tops and further increase high-level cloudiness through the cirrus shields formed by their outflow. More intense synoptic-scale vertical motions from the greater rainfall of a warmer climate could also reduce cloudiness, but could increase cloud heights (e.g., Schneider et al., 1978; Wetherald and Manabe, 1980). One popular idea is that fractional changes would be compensated by height changes so that little net effect would be realized (e.g., Cess, 1976; Wetherald and Manabe, 1980; Cess et al., 1982).

The net effect of the various possible changes in cloud properties can only be examined by physical models for clouds coupled to atmospheric dynamics in a three-dimensional context. We now turn to discussion of three-dimensional climate general circulation models.

5.4.8 General Circulation Models

General Circulation Models (GCMs) have evolved as a generalization and by-product of the development of numerical weather prediction models. They consider the atmosphere in three spatial dimensions and time. This domain is represented either in terms of a mesh of points or in terms of polynomial (e.g., spherical harmonic) basis functions. The GCMs solve jointly the equations of motion for atmospheric winds and equations for conservation of thermal energy and water vapour, including transport by the calculated atmospheric motions. The equation for thermal energy includes: detailed treatments of the vertical radiative transfer of solar and longwave radiation; parameterizations for moist and dry convective or turbulent redistribution of thermal energy and moisture. The equation for water vapour has an evapotranspiration source at the Earth's surface and a sink through formation of rain or snowfall.

 The atmospheric model depends on boundary conditions or on other models at the Earth's surface. For example, an ocean model is required to provide ocean surface temperature since the atmosphere and climate, in general, are strongly coupled to ocean surface temperatures. Also necessary are models for sea ice and for various land-surface processes including snow cover, soil moisture, and evapotranspiration. Figure 5.1 shows schematically the various linkages treated by GCM climate models.

Figure 5.1 Schematic description of the structure and processes of GCM climate models

Only the GCMs among climate models can plausibly model such atmospheric surface variables as soil moisture, snow cover, and ground temperature. On the other hand, some of the current deficiencies and uncertainties in GCM climate projections stem from use of much cruder models for surface climate processes than are used for the atmosphere. Now we turn to this question of model deficiencies.

5.5 MODEL DEFICIENCIES

5.5.1 Relationships Between Different Kinds of Models 

The radiative-convective models have traditionally been used to examine the most accurate and computationally expensive schemes for atmospheric radiative transfer. They have also been used to explore cloud-radiation feedbacks as discussed earlier. For clear-sky conditions, the radiative transfer aspects of GCMs are believed to be now more accurate than most other features in the models and are being further refined and validated. Furthermore, cloud formation and vertical convective energy transfers are essentially of a short time scale and three-dimensional in nature, and so in principle require (as a minimum) a GCM for their direct calculation. Likewise, the transport and ice-albedo parameterizations of energy-balance climate models are superseded by their potentially much more realistic treatments in GCMs. Furthermore, only GCMs are capable of providing information useful for evaluating potential impacts of future climatic change, that is, details regarding regional climatic change and changes in surface hydrological processes.

For these reasons, the simpler climate models, in principle, have no additional capabilities for projecting future climatic change besides that of the GCMs. In practice, some aspects of some GCMs may be less satisfactory than corresponding treatments in simpler models. The most obvious example of this principle has been past GCM studies of climatic change with fixed ocean temperatures. These studies found much smaller values for global warming than suggested by the one-dimensional climate models which more realistically allowed effective ocean temperatures to vary with climatic change.

Even today, most GCMs include 'swamp' or 'mixed-layer' ocean models that assume zero horizontal transport of heat by oceans. An energy balance model with a more realistic ocean heat transport characterization might in some ways be regarded as more correct than such GCMs for future climate projections. Furthermore, the developers of simple climate models often pay much more attention to observations constraining their models than do developers of GCMs, in part because there is such a vast range of possible data that could be used to validate a GCM. Thus, observational or physical constraints (e.g., Eq.(5.1)) have often been formulated first in simple models before application by GCM modellers.

In spite of the above considerations, it is most useful here to examine primarily the deficiencies of GCMs. One of the general deficiencies of GCMs is that their horizontal mesh scales are several hundred kilometres or larger because of computer expense. Thus, much regional climate detail cannot be resolved. Better climate model resolution might improve the simulation of larger scale features even more than features at the limit of resolution. Mesoscale climate models could be embedded within GCMs to attempt description of scales down to order of 100 km, but this procedure has not yet been applied to questions of future climatic change. It will not be discussed further here. The other presently most obvious deficiencies in GCM simulations of future climate are examined in the following sections.

5.5.2 Clouds 

As discussed earlier, future changes in cloud properties could make either large increases or possibly large decreases in the net radiation budget of the climate system and hence could either amplify or diminish (but not cancel entirely) the effect of increased CO₂ and other trace gases. Regional changes in climate would result from changes in cloud radiative effects coupled to shifts in quasi-stationary planetary waves (e.g., Trenberth, 1983; Hartmann, 1984). General Circulation Models have attempted to generate cloudiness but with little confidence in the result. In particular, several models have simulated cloud formation for present and future climates by assuming that clouds form whenever the model precipitates, or whenever moist convection occurs in the model or according to the relative humidity (e.g., Wetherald and Manabe, 1980; Washington and Meehl, 1983, 1984; Hansen et al., 1984). Wetherald and Manabe have suggested mechanisms for reduction of clouds in low latitudes and increased stratus in high latitudes in response to global warming.

There are several serious difficulties in including clouds in models. First, cloud properties are largely subgrid-scale. Even the most regular layered cloud systems have wide variations on a 100-km scale, and boundary-layer cumulus clouds can be of a scale less than 1 km. The thickness of stratus clouds may be much less than the vertical grid interval.

Second, there is a wide variety of cloud types, each of whose radiative properties varies widely from cloud system to cloud system. Thus, any binary yes-no description of cloud cover is too oversimplified to be useful. Different physical models are required for different cloud types. These models must satisfactorily give all the radiatively important cloud properties, in particular, fractional cover, height, liquid water content, drop sizes, and spatial scale. It is necessary to model these properties with enough attention to physical processes that their change with climatic change can be adequately projected. Modellers, in particular, recognize the need for separate models of high clouds, such as cirrus, boundary-layer clouds, trade-wind region stratocumulus, frontal-layer clouds, and clouds associated with deep cumulus convection. Cloudiness on the margins of the Arctic and Antarctic ice packs in spring and summer is especially important for determining the magnitude of ice-albedo feedback.

The third, and perhaps most serious difficulty, is that processes of cloud formation and cloud radiative properties have not been satisfactorily related observationally to other meteorological processes. Diurnal variations of cloudiness are poorly understood but may be important for determining changes in the radiation balance. The existing climatologies of cloud cover are of somewhat marginal value for the purpose.

As a consequence of the limitations discussed above, the current approach of modellers is to make up some 'cloud model' based on simple physical arguments, include this parameterization in a GCM simulation, and compare the resulting model cloud climatology with one or several observational climatologies. Such procedures are unsatisfactory because (1) they are usually only validated against fractional cloud cover, which is but one of the radiatively important cloud properties; (2) there can be large differences in cloud cover climatologies so that it is not difficult to find at least some data that the model clouds appear to agree with; and (3) since cloud parameterizations usually have one or more adjustable parameters, it is possible for models to agree with present data sets without the cloud model responding properly to climatic change.

5.5.3 Ocean Coupling 

The climate warming by increased CO₂ depends in large part on increases in ocean temperatures. The oceans are also important for their uptake and storage of CO₂ as discussed further in Chapter 3. The oceans are as complex a dynamical system as the atmosphere and observationally more poorly characterized. Ocean surface temperatures are determined by the balance between spatially varying net surface heating and a variety of dynamical processes for the redistribution of thermal energy, including small-scale vertical mixing and large-scale horizontal transport by ocean currents (Bretherton, 1982; Woods, 1984). There are not yet available ocean GCMs with enough spatial resolution to resolve the energy-containing eddies as done in GCMs for the atmosphere. Rather, at present the most sophisticated ocean models for climate studies (e.g., Bryan et at., 1982) are of coarse resolution (compared to ocean eddies) and heavily influenced by semi-empirical eddy diffusion parameterizations. Even the coarse-resolution ocean models are not yet being employed in most GCM studies of future climate.

Rather, GCM studies to date have largely assumed 'swamp' or 'simple mixed-layer' ocean models. Both kinds of models neglect entirely horizontal energy transport by the oceans. The swamp model characterizes the ocean surface as a wet surface of zero heat capacity, whereas the mixed-layer models assume an ocean reservoir for heat, uniformly mixed in the vertical. The ^'swamp model' ocean evaporates water and conserves energy but is otherwise highly unrealistic. The heat capacity of the 'mixed layer' model can be adjusted to give a reasonable range of temperatures for the annual cycle. However, the lack of horizontal heat transport by the oceans is quite unrealistic and gives serious difficulty in modelling other important processes such as formation of polar sea ice. Since up to half the total heat transfer is in reality accomplished by the oceans, either the model heat transport is reduced and the pole-equator temperature difference in the model becomes larger than in reality, which seems not to be the case, or atmospheric transport is increased which must influence atmospheric flow patterns significantly.

A conceptual improvement upon the swamp and simple mixed-layer models that is computationally not much more complicated is to constrain the ocean horizontal heat transport or temperature gradients to correspond to observation or some other prescribed relationship. The study by Hansen et al. (1984) uses a fixed horizontal heat transport mixed layer ocean model. Hoffert et al. (1983) argue that ocean transport may act to minimize tropical surface temperature changes. Realistic patterns of ocean temperature change may be important for determining shifts in rainfall patterns, especially in the tropics.

5.5.4 Sea Ice 

As discussed earlier, simple climate models show that the albedo decreases from reduction in the cover of snow and ice can significantly amplify the climate warming of increased CO₂, i.e., reduce in Eq. (5.1). This feedback mechanism has also been included in GCM studies but not necessarily with careful attention to physical realism. It appears (e.g., Robock, 1983a; Hansen et al., 1984; Washington and Meehl, 1984) that changes in sea-ice cover are the major contributor in a seasonal cycle model to the albedo-feedback mechanism and depend on the seasonal variation of the effective thermal inertia at the sea-ice margins. Sea-ice cover persists into spring and summer or later, whereas most land snow cover melts sooner, and where shaded by tall vegetation, provides much less albedo contrast.

There have been at least four basic deficiencies in GCM treatments of sea-ice(1) lack of realistic ocean heat transport, as already discussed, (2) unrealistic treatments of the albedo of sea ice, as discussed in the next section, (3) unsatisfactory models for cloud properties at the sea-ice margins as earlier discussed, and (4) oversimplified models of the thermodynamics and dynamics of the sea-ice itself (improvements are suggested by Semtner, 1984; Hibler, 1984; Hibler and Bryan, 1984). Treatments of the effects of leads and turbulent transport at the water-ice interface are inadequate. Other questions of possible deficiencies, such as whether GCMs give a realistic description of sensible fluxes between sea ice and atmosphere, also need examination.

5.5.5 Surface Albedos

Both the numerical and conceptual bases for specifying surface albedos in GCMs have been deficient. That is, numbers have been used for model albedos inconsistent with the available observational studies, and possible changes in surface albedo with climatic change have not been included beyond a crude treatment of albedo change from change in snow and sea-ice cover. Furthermore, the observational basis for parameterizing surface albedos in GCMs is inadequate.

Except for the effects of snow and ice, surface albedo changes may be small but may still need consideration. For example, ocean albedos depend on bubbles and turbidity of the surface water and on the angle between solar beam and water interface. Thus, ocean albedos vary with solar zenith angle, scattering of the solar beam by cloud particles, and wave spectrum, as well as varying with the amounts and nature of particles in the water, such as phytoplankton. At least some of these dependencies may imply significantly different ocean albedos with future climatic change.

Land surface albedos are much more complex and dependent on atmospheric conditions and surface microclimates. There are large variations of these albedos with wavelength of the solar beam as well as with the solar zenith angle. Theoretical characterization of the albedo of vegetation canopies includes a complicated problem in radiative transfer. Soil albedos depend on soil moisture and on soil chemical and physical structure. As an example of the level of detail regarding land albedos actually used in current GCM studies of future climate, Washington and Meehl (1984) assume a value of 0.13 for all non-snow-covered land surfaces, except deserts for which they use 0.25.

Perhaps improved model descriptions of most aspects of surface albedo are currently not warranted considering the large uncertainties regarding changes in cloud optical properties. The same argument could be made to justify current model neglect of atmospheric aerosol radiative effects. However, more refined treatments of snow and ice albedo properties would certainly increase confidence in the model sensitivities to ice-snow feedbacks. For example, Manabe and Stouffer (1980) do not even distinguish between the albedos of snow-covered and snow-free ice. Except for Hansen et al. (1984), GCM studies of future climate have not even included the reduction of snow surface albedo by tall vegetation.

5.5.6 Land Surface Hydrology

Water in liquid and solid form is deposited by actual and GCM atmospheres on the land surface. The subsequent disposition of this water is a major factor in determining regional climates. Snow surfaces melt and change their albedos in complicated ways that have been studied by snow hydrologists. Yeh et al. (1983) have shown with a GCM simulation that removal of snow cover in early spring would give greater continental dryness that persists into late summer.

Some of the water incident at the surface is intercepted and re-evaporated by the foliage of vegetation (e.g., Shuttleworth and Calder, 1979), some runs off on the surface, some infiltrates into the soil where it provides water for plant transpiration, some re-evaporates at the soil surface, and some percolates to below the root zone where it supplies the subsurface water reservoirs and hence the 'base flows' of drainage basins. The effects of vegetation changes on evapotranspiration have recently been reviewed by McNaughton and Jarvis (1983). A model for a vegetated surface coupled to a planetary boundary layer model has been discussed by DeBruin (1983). Shukla and Mintz (1982) have demonstrated that changing GCM land surfaces from completely wet to completely dry gives a large decrease in rainfall over land. Many other recent studies demonstrating the sensitivity of rainfall to evaporation parameterizations have been reviewed by Mintz (1984).

The maximum rate of infiltration is limited by the soil hydraulic conductivity and so can vary widely over small distances. The amounts of water infiltrated depend strongly on the distribution of precipitation in time and space. That is, surface runoff may be very different for an intense localized convective storm than it is for a uniform drizzle, although these two situations have the same rainfall over a GCM grid square and averaged over a day. From the viewpoint of climate impacts, this difference could determine whether a farmer has a well-watered crop or, conversely, whether much of his soil ends up in the river and his land is subject to drought. From the viewpoint of atmospheric climate, the subgrid-scale structure of rainfall has a significant influence on how much water the land surface can return to the atmosphere through evapotranspiration.

All the above questions are neglected in current GCM treatments of surface hydrology. The conventional GCM treatment of soil water is to assume that the soil acts as a bucket which after being filled adds its surplus to runoff. The full bucket evaporates as would a moist surface until it has lost some fraction of its capacity. At lower levels of water in the bucket, evaporation is assumed to be linearly proportional to its remaining water content. Variations in surface roughness because of differing vegetation cover are usually neglected. The model of Hansen et al. (1984) elaborates on this scheme somewhat by use of two soil reservoirs whose capacity depends on vegetation type. However, the details of their formulation are somewhat arbitrary.

It may be that the present GCM treatments of land-surface processes are adequate for making first estimates of future regional climatic change. On the other hand, it could turn out that more refined treatments (e.g., Dickinson, 1984) may be necessary. It must be kept in mind that land-surface processes can only be properly modelled in GCMs which give realistic simulations of precipitation and which include other realistic details, in particular, a good model of the planetary boundary layer and a diurnal cycle of radiation. Both these latter factors are lacking in most of the GCMs currently used to study future climate. Furthermore, the dependence of surface hydrology on the subgrid-scale details of rainfall intensities is of especial concern since these details could change significantly with a warmer climate. Better descriptions of river discharge may be important, especially for modelling changes in the Arctic Ocean. More attention must be given to surface radiation depending on cloudiness as well as temperature, and to relative humidity in the models since these not only are important for evapotranspiration but for plant growth in general.

5.5.7 Transient Response 

Most GCM studies of the climate response to a CO₂ warming have considered the steady-state response for a given increase in CO₂, in particular, a doubling or quadrupling of CO₂. It is fortunate that this has been the tack, for standard benchmark calculations are required to make comparisons between different models and to help focus attention on various model deficiencies. However, the results of a steady-state calculation may be misleading in application to estimating the actual climatic change caused by human activities at present or in the future. Emissions of CO₂ into the atmosphere are not fixed but growing, since 1973 at a rate of somewhat less than 2% a year (Carbon Dioxide Assessment Committee, 1983), and atmospheric concentrations have been growing by about 0.4% per year.

The oceanic surface mixed layers with depths of 50100 m equilibrate with atmospheric temperatures on a time scale of several years. However, high-latitude oceanic convection mixes surface waters in contact with the atmosphere to great depths in the ocean. Consequently, an ocean reservoir of order of 1 km in depth, depending on the time scale of the warming, must be warmed before ocean surface waters can equilibrate with the atmosphere. Roughly 50 years are required for the atmosphere to nearly equilibrate with this reservoir; equivalently, the actual temperature response to CO₂ warming may lag the steady-state response by up to several decades, or at any one time have a magnitude not much larger than half the steady-state response. Obtaining the details of the transient response to CO₂ warming would require a satisfactory ocean general circulation model, a tool not yet available as discussed earlier. However, estimates of the time scale involved can be made using studies of ocean tracers (e.g., Broecker et al., 1979) if buoyancy effects of thermal anomalies can be neglected. Energy balance model studies of the transient response have been discussed by Robock (1978), Schneider and Thompson (1981), Cess and Goldenberg (1981), Dickinson (1981b), Michael et al. (1981), Schlesinger (1983a), Hansen et al. (1984), Wigley and Schlesinger (1985), and Harvey (1985).

The transient response to CO₂ warming differs from the steady-state response not only in overall magnitude but also in the latitudinal and regional details. This assertion follows from the different, probably slower, response times for high latitudes compared to low latitudes. Both the deep oceanic convection and the ice-albedo feedbacks act to retard the high-altitude response more than elsewhere. The question of how far the transient response departs from the steady-state one as a function of latitude is controversial and different conclusions have been drawn (e.g., Schneider and Thompson, 1981; Bryan et al., 1982; Thompson and Schneider, 1982; North et al., 1984). Better estimates of ocean heat uptake will likely require further progress in the development of detailed models of ocean circulation.

5.6 MODEL LIMITATIONS

5.6.1 Validation and Performance of Control Runs

 The GCMs are the most complete simulation tools for the climate system. However, the models that have so far been used to study CO₂, warming are crude and incomplete descriptions of many important climate processes. These difficulties arise in part because of the limits of the models' spatial resolution. There will probably always remain some questionable aspects of model formulations. Yet many deficiencies may make little difference in projections of future climate. Furthermore, physically more complete descriptions are usually more complicated and more difficult to understand than are simpler parameterizations, hence also more susceptible to serious logical or programming errors in their formulation.

Thus, it is necessary to find means to obtain more precise estimates of the reliability of the results of the limited models that are available now or would be at any time, and so, hopefully, to increase our confidence in them. One approach for doing this is to compare model simulations with observed climate. In particular, the models should be able to reproduce the observed spatial and seasonal variations of climate.

The GCMs are able to reproduce the large seasonal variation surface air temperature changes of the Northern Hemisphere continents, e.g., Manabe and Stouffer (1980). Their simulation of global average surface temperatures and pole-to-equator temperature differences has also been in surprisingly good agreement considering the lack of ocean heat transport. The control model of Hansen et al. (1984) apparently gives a good simulation of the observed seasonal variation of sea ice in both hemispheres (Barry et al., 1984), presumably because of the adjustment of prescribed ocean heat transport to provide such agreement.

Many parameters in the GCMs have somewhat arbitrary magnitude and are 'tuned' to satisfy observational constraints. Thus, for example, agreement between modelled and observed cloud cover or radiation fluxes at the top of the atmosphere is usually in part the result of adjustment of cloud parameterization parameters to achieve such agreement. While such tuning is a necessity, the consequent agreement with data does not help validate the model's performance as would agreement with data that had not been used to develop the model. Furthermore, model results may deteriorate with physical improvements in other parameterizations because of removal of compensating errors. Another good check of a model's surface physics and planetary boundary-layer parameterizations in response to large radiation changes would be an agreement for different land surfaces between model and observed diurnal cycle of temperature. Most current GCMs, however, do not have a diurnal cycle of radiation. Agreement between modelled and observed diurnal cycle would likely be poor for GCMs without adequately realistic treatments of the planetary boundary layer and surface energy transfer processes.

Another approach to model validation is to see the extent to which past climates can be modelled. Unfortunately, the data regarding past climates are not sufficiently complete to allow any unambiguous model testing. Times of large difference from present conditions may be most appropriate for such tests. Several studies have been made of GCM simulations of the last ice age at 18K BP (i.e., 18,000 years ago). However, these studies failed to provide much model validation since they used mostly available data for boundary conditions. Hansen et al. (1984) considered the question of global energy balance in their 18K BP simulation, with prescribed ocean surface temperatures and ice sheet. They found the radiative fluxes at the top of the atmosphere to be somewhat negative relative to current conditions. They concluded that either the positive cloud feedback in their model was somewhat exaggerated or that some of the boundary conditions they used, perhaps the assumption of 200 ppmv CO₂ concentration or tropical ocean temperatures, were somewhat in error. Broecker and Takahashi (1984) have reviewed possible mechanisms for changing atmospheric CO₂ on a time scale of ice ages.

The most documented periods of past climates which were much warmer than present are the early Holocene post-glacial epoch 6000 to 9000 years ago, with observations indicating local summer temperatures at times at least l to 2 ^°C warmer than present, and the Cretaceous period about 100 million years ago with temperatures 10-20 °C warmer. GCM simulations of 9K BP with changed orbital parameters have been discussed by Kutzbach and Otto-Bliesner (1982).

Barron and Washington (1984) have discussed simulation of Cretaceous climate. The latter study found that changes in model geography were inadequate to explain the observed Cretaceous warmth and hence invoked some additional heating, possibly that due to more atmospheric CO₂ then than now. Berner et al. (1983) have shown that atmospheric CO₂ could vary by at least an order of magnitude on a time scale of tens of millions of years as a result of shifting balances between geophysical sources and sinks. Studies of past climates do not provide much direct model validation because of the presence of additional very long time scale feedbacks, such as natural changes of CO₂ concentrations which may be invoked for removing differences between model and observations. However, simulation of the climate of the last ice age may be useful in validating overall model feedback since estimates of CO₂, ocean temperatures, and ice sheet geography are available. More generally, any studies which require comparisons between model output and observations are likely to improve our understanding of model capabilities.

5.6.2 Signal-to-noise Problem

GCMs simulate climate as an average of day-to-day weather fluctuations and other aspects of natural variability. Thus, just as actual climatic change is obscured by natural variability (e.g., Leith, 1973; Madden and Shea, 1978), so are the climatic changes obtained by GCMs for increased CO₂. The problem is one of obtaining the climatic change signal in the presence of model noise. In principle, models can generate much more extensive climatic statistics than are available for the past actual climate. However, since GCMs require large computing resources, in practice, the length of time period for which they can simulate climate is limited to at most a few decades. Over such a time period, only relatively large climatic change (e.g., that associated with doubling or quadrupling atmospheric CO₂) can be established over the model noise background. The climatic change up to 1985 due to the previous increase of CO₂ is at least a factor of five smaller than that due to doubling. To estimate this relatively small change with reasonable statistical significance would likely require at least ten model simulations of climate starting perhaps 50 years ago.

Perhaps when the speed of supercomputers has increased 100-fold over current values, such integrations might be practical. Such increases in computing power may be available in the 1990s. However, it is also desirable to develop GCM climate models with higher spatial resolution, which is also now limited by lack of computing resources. Thus, the problem of distinguishing model signals from noise will probably not diminish greatly with future computers.

The most widely applied statistical approaches to the GCM noise problem have been univariate. That is, changes in the value of each variable at each gridpoint are separately tested for statistical significance (e.g., Chervin and Schneider, 1976; Chervin, 1980, 1981; Hayashi, 1982; Katz, 1982, 1983). There are various recognized difficulties with this approach (e.g., as discussed by Hasselmann, 1979), the most obvious of which is that, if testing for significance at a 95% confidence level, 5% of the gridpoints will on the average be falsely identified as significant. Hayashi (1982) suggests an emphasis on confidence limits rather than on significance testing. Livezey and Chen (1983) have discussed possible approaches for testing the statistical significance of changes in meteorological fields accounting for their multiplicity and spatial correlations.

5.6.3 Regional Continental Scale Details

It has long been recognized that the most useful information on future climate would necessarily involve changes on a regional-continental scale of typically 1000 km or so over the continental areas where the bulk of population and economic activities is found. If GCM climatic change integrations are carried out for a sufficient time to overcome the signal-to-noise problem, regional-scale climatic change features can be found. However, at present, we can have little or no confidence in the reality of such features as a description of expected future climate, for several reasons. First, careful validation of GCM simulations of present regional-scale features is lacking. Second, shifts in continental-scale features are dependent on dynamical and physical details poorly treated in GCMs. These might include, for example, shifts in the stationary planetary wave structure and associated shifts in radiative sources and sinks (e.g., as discussed by Hartmann and Short, 1979; Hartmann, 1984).

Considerable effort will be needed to establish the physical, as contrasted to statistical, validity of GCM simulations of regional climatic change. One possible approach is to compare similarities and differences between different model simulations. There are considerable duplications between models in questionable parameterizations, but there are also many differences. Disagreements between different models can be used to help flag uncertainties of model projections of future climate.

5.7 REVIEW OF GCM RESULTS FOR INCREASED CO₂ 

5.7.1 The More Realistic GCMs

Here we compare results from recent GCM simulations of the climatic change from increased CO₂. It is useful to distinguish between exploratory GCMs and the more realistic GCMs. The most realistic GCMs have annual cycles and realistic continents and orography within the constraints of model resolution. They should also have adequate horizontal and vertical resolution. What is adequate resolution needs to be established by comparison of model simulations not just with observations but also with higher resolution simulations with the same model. The most satisfactory models, according to these considerations, are the models of Manabe and Stouffer (1980) and Washington and Meehl (1984). Also included is the model of Hansen et al. (1984) which, although coarse in its horizontal resolution, appears to have adequate baroclinic wave variability (Hansen et al., 1983) and possibly does a superior job on some aspects of climate simulation. All the models suffer from probably inadequate planetary boundary-layer parameterizations and resolution. Their vertical resolution around the tropopause is also questionable. They may extend insufficiently far into the stratosphere for realistic planetary wave structures. Other model features are summarized in Table 5.2.

All the models referenced above are formulated to maintain global average radiative equilibrium as required to be able to estimate global average temperature change. Another informative approach is to use observed ocean temperatures for a control simulation and to take ocean surface temperature changes as prescribed rather than calculated, but changing with increased CO₂ as inferred from previous integrations and energy balance criteria and consistent with GCM simulations that do calculate ocean temperature change. This has been done by Mitchell (1983), who assumed a constant ocean temperature change of 2 °C along with doubled CO₂, and by Mitchell and Lupton (1984) who assumed quadrupling of CO₂ and prescribed ocean temperature changes for each latitude belt that would seem to imply approximately no change in oceanic heat transport. Continental-scale variations in the climate response in these studies may be less confused by errors in the control simulation than in studies which assume mixed-layer ocean models for both control and perturbation simulations.

Large quantities of diagnostic information are generally reported by authors of GCM studies. We consider here only some features that are of practical importance in interpreting the surface climate simulations. Note that Manabe and Stouffer assumed a quadrupling of CO₂ whereas the other studies a doubling. Figures 5.2 to 5.6 compare the calculated temperature change for increased CO₂. Figures 5.2 and 5.3 show the zonal average temperature change as a function of altitude for the Washington and Meehl and the Manabe and Stouffer models, respectively. The results differ most in the stratosphere where the Manabe and Stouffer model shows about twice as large a temperature decrease. This is not surprising considering that it assumed twice as large CO₂ increase. What is more surprising is the similarity of the troposphere change. The Manabe and Stouffer model surface temperature is evidently about half as sensitive to external heating ( twice as large) as the Washington and Meehl model, as shown by the fact that global average surface temperature increase for both models was about 4 °C. Both models show largest warming in the Northern Hemisphere in winter in high latitudes. In the Southern Hemisphere, however, the Washington and Meehl model shows largest warming at the edge of Antarctica, whereas the Manabe and Stouffer model shows a less intense maximum warming centred over the South Pole. Figure 5.4 bottom frame, shows annual average temperature change contours for the Hansen et al. model. This model gives greater warming in the tropical troposphere, nearly double that of the other two models but shows relatively small annual mean polar amplification. Their global average warming is also about 4 ^°C. The model details responsible for significant differences between outputs are not known. However, 'causes' for differences in global temperature change can be diagnosed in terms of differences in feedbacks as discussed further in Section 5.8.

Table 5.2 Comparison of some features of the models of Manabe and Stouffer (1980), Hansen et al. (1984), Washington and Meehle (1984) 

Figure 5.2 Zonal average temperature change in ^°C versus altitude and latitude for a steady-state doubling of CO₂ according to the model of Washington and Meehl (1984). Top frame is for December to February; bottom frame is for June to August. Cooling in the stratosphere is shaded

Figure 5.3 Same as Figure 5.2, except for quadrupling of CO₂, according to Manabe and Stouffer (1980). Cooling in the stratosphere is indicated by a dot pattern. Regions of warming greater than 4 ^°C are shaded 

The upper frame of Figure 5.4 shows the geographical distribution of the annual mean Hansen et al. surface warming. No obvious pattern is seen beyond the fact that the high-latitude warming appears to be somewhat larger than that seen in the bottom frame, which only extends to the lowest model layer and does not include surface air temperatures. The 2 ° change contained in the bottom frame over the South Pole which especially gives this impression is not actually found but is the result of a minor glitch in the plotting program (Hansen, personal communication). The middle frame shows the seasonal variation of the zonal average warming. Largest warming is seen in high latitudes in winter of both hemispheres, in qualitative agreement with the other models being discussed, and very little warming at the same latitudes in summer. For comparison with the upper two frames of Figure 5.4, Figures 5.5 and 5.6 show the geographical distribution of surface warming averaged over DecemberFebruary and JuneAugust for the Washington and Meehl and the Manabe and Stouffer models, respectively. Figure 5.5 shows very large temperature changes in the winter season in the North Atlantic and North Pacific and the Southern Ocean around Antarctica. By contrast, the Manabe and Stouffer model has a Northern Hemisphere maximum winter temperature increase occurring in the Arctic Ocean and high-latitude continental areas, especially Northern Siberia. Their Southern Ocean temperature increase is less than that over the Antarctic continent which, in turn, is less than the Washington and Meehl Southern Ocean warming. Elsewhere, Figure 5.5 shows the largest temperature increase of up to 8 ° over summertime Australia, whereas Figure 5.6 shows summertime maximum increases greater than 6 ° in Central Asia and Eastern North America.

Figure 5.4 Air temperature change in °C for doubling of CO₂. according to Hansen et al. (1984). The upper graph shows the geographical distribution of annual mean surface air warming; the middle graph shows the seasonal variation of the surface air warming averaged over longitude, and the lower graph shows the altitude distribution of the temperature change in model layers averaged over season and longitude

One climate feature of high latitudes of considerable importance for determining model response is the extent of sea ice. Sea ice determines in large part the icealbedo feedback in a GCM since sea ice persists into the spring and summer seasons of greatest solar irradiance. Figure 5.7 shows the sea ice obtained by the Manabe and Stouffer model for their control study in comparison with observed coverage. In the Northern Hemisphere, their modelled sea ice is close to that observed in summer and is in considerable excess of that observed in winter. By contrast, in the Southern Hemisphere their sea ice is less than half of that observed in winter and practically disappears in summer. Figure 5.8 shows the sea-ice extent obtained by Washington and Meehl for their control and doubled CO₂ calculation. Their control sea-ice coverage is higher than observed in both hemispheres and both seasons and appears to have less seasonal variation than that observed, as shown in Figure 5.7. In particular, the model Norwegian Sea and all the Arctic Ocean are completely filled with ice in summer, whereas in reality the summer sea ice recedes at least 15° poleward into the Barents Sea. It should be noted that this comparison is somewhat unfair since the model results show sea-ice extent averaged over the three summer months rather than for August when sea ice is near its minimum. Nevertheless, the model summer Arctic ice appears to be at least as extensive as the observed winter maximum extent. In the Southern Hemisphere, the model sea ice in both seasons extends to about 55 ° S, about 5 ° farther than observed in winter and 10° to 15° farther than observed in summer. Hansen et al. use two control simulations, whose annual mean sea ice is compared with observations in Figure 5.9. Their standard control was reported to have 15% less sea ice than seen in observations with an especially noticeable deficit at longitudes around 100° W and 50° E in the Southern Hemisphere. They produced an alternate control with a different assumption concerning sea-ice melting that gives 23% greater sea-ice cover than observed.

Figure 5.5 Same as Figure 5.4 (upper frame) for steady-state doubling of CO₂ (Washington and Meehl, 1984), except showing winter and summer of surface air temperature change in °C

Figure 5.6 Same as Figure 5.5 but for quadrupling CO₂ (Manabe and Stouffer, 1980), showing a geographical distribution of surface air temperature change. Regions of warming greater than 5° are shaded

The role of sea ice in icealbedo feedback for model CO₂ warming is indicated by Figures 5.10 and 5.11. Figure 5.10 shows the change in planetary albedo for the Washington and Meehl model. Extensive areas of albedo decrease of greater than 0.05 are seen in both hemispheres and for both seasons along the model sea-ice margins but nowhere else. During the summer period, a belt of albedo change greater than 0.2 at the top of the atmosphere surrounds the Antarctic continent at a latitude of about 60^° S, apparently equatorward of any real sea ice at that time. Figure 5.11 shows separately for continent and ocean the seasonal variation of increase in absorbed solar radiation for the Manabe and Stouffer model. Over the oceans, they find the most extensive large change in the Northern Hemisphere centred at 70° N. In the Southern Hemisphere, their largest change is at the edge of the Antarctic continent in the spring season. By summer, their change in absorbed solar radiation has dropped to small values consistent with the absence of control sea ice at that time.

 Figure 5.7 Distribution of sea-ice cover for February and August for the 1 x CO₂ control simulation from Manabe and Stouffer (1980) shown by dotted and hatched areas, with the observed distribution quoted by them indicated by the heavy dashed-dotted lines

Figure 5.8 Distribution of sea-ice extent for 1 x CO₂ (solid lines) and 2 x CO₂ (dashed lines) for DecemberFebruary (top frame) and JuneAugust (bottom frame), according to Washington and Meehl (1984)

Figure 5.9 Annual mean sea-ice cover according to Hansen et al. (1904). Frame (a) is observations, (b) is the standards 1 x CO₂ control, and (c) is the alternate control

Figure 5.10 Top of the atmosphere albedo change in percent for 2 x CO₂ 1 x CO₂, DecemberFebruary and JuneAugust, according to Washington and Meehl (1984)

Figure 5.11 Latitudeseason plots of change in absorbed solar radiation for 4 x CO₂ - 1 X CO₂, according to Manabe and Stouffer (1980)

Planetary and surface albedo annual average change calculated by the Hansen et al. model is shown in Figure 5.12. Their surface albedo plot indicates a large sea-ice-associated surface albedo change in both hemispheres. However, their planetary albedo plot shows hardly any sea-ice-associated concentration of albedo change in the Northern Hemisphere. Along Antarctica in the Western Hemisphere, there is a stretch of albedo decreases greater than 0.05 at the top of the atmosphere, a much smaller change than that seen in the Washington and Meehl plot, Figure 5.10.

Figure 5.12 Annual average albedo changes in per cent for 2 x CO₂ l x CO₂, according to Hansen et al. (1984). Top frame is surface albedo; bottom frame is top of the atmosphere albedo

Figure 5.13 Same as Figure 5.2 for doubling CO₂ (Washington and Meehl, 1984), except the plot shows fractional changes in cloud cover

Figure 5.14 Same as Figure 5.4 for doubling CO₂ (Hansen et al., 1984), except the plot shows per cent change of cloud cover

Figure 5.15 Geographical distribution of soil moisture change in cm during JuneAugust in the Manabe and Stouffer model for 4 x CO₂ l x CO₂. The upper figure shows the result of a simulation with a comparatively low resolution (15 waves for both longitude and latitude) and the lower figure a simulation with a higher resolution (21 waves). (Manabe et al., 1981)

Another climate feature of considerable importance for inferring changes in surface heating is the calculated change in cloudiness. The Manabe and Stouffer study avoided this issue by prescribing clouds to be independent of longitude with latitudinal variation based on observation. Figure 5.13 shows the change in cloudiness calculated by Washington and Meehl for the December-to-February and June-to-August periods. They find a slight decrease of cloudiness in low latitudes at all levels in the troposphere and a predominance of small increases in high latitudes. These high-latitude increases become relatively large around the tropopause at the top model level with clouds. These changes in cloudiness have some positive effect on the model global radiation balance and hence global surface warming, as discussed later. Figure 5.14 shows the cloudiness change found by Hansen et al. The top frame shows the annual mean geographical distribution of total cloudiness change, the bottom frame the annual mean vertical distribution of cloudiness change, and the middle frame the seasonal variation of total cloud-cover change. They find decreases in cloudiness of several per cent or more at most levels, latitudes, and seasons. Increases are seen for low-level clouds in high latitudes and high clouds in middle latitudes. This latter change resembles somewhat the high-level cloud change found by Washington and Meehl. The cloud changes found by Hansen et al. are evidently large enough to be responsible for a major amplification of their surface warming as discussed later.

Figure 5.16 From Manabe and Stouffer (1980). Latitude-time distribution of zonal mean difference in soil moisture in cm over continents for the 4 x CO₂ 1 x CO₂ experiments. Note that the maximum moisture storage in this study is assumed to be 15 cm everywhere

Another important climate feature calculated by the GCMs is change in soil moisture. Although obtained very crudely, it does represent the balances between model precipitation versus evaporation and runoff. Manabe et al. (1981) have analysed the soil moisture change of the Manabe and Stouffer study and that of a somewhat higher resolution version of the same model. Their results for the Manabe and Stouffer model are shown in Figure 5.15 for the Northern Hemisphere summer period. Although there is some variation between models and considerable sampling error, there is a predominance of soil moisture decrease in the Northern Hemisphere during the summer season and in middle and high latitudes. They find some highlatitude regions of increased soil moisture. This summertime drying of land north of 30° N is also seen in Figure 5.16 which shows their seasonal variation of longitudinally averaged soil moisture change. Qualitatively similar results were obtained using an idealized geography sector model discussed further below (Manabe et al., 1981; Wetherald and Manabe, 1981).

The results of Washington and Meehl (Figure 5.17), on the other hand, show a predominance of increased soil moisture over most extratropical continental areas in the Northern Hemisphere for all seasons. They do find a small tongue of drying reaching from Southern California to the Central Great Plains of the United States and reduced soil moisture over Southeast Asia and much of Africa south of the Sahara. The seasonal variation of longitudinally averaged soil moisture according to Washington and Meehl is shown in Figure 5.18. This plot shows increases in continental soil moisture between 30° and 60^° N with greatest increases in the winter and spring seasons. Decreased soil moisture is found for most latitudes and seasons in tropical latitudes and the Southern Hemisphere. The model results of Hansen et al. do not indicate a substantial drying in spring and summer in middle-to-upper midlatitudes (Rind and Lebedeff, 1984, p. 54). The calculation of Mitchell and Lupton (1984), shown in Figure 5.19, does give the same general soil moisture patterns as obtained by Manabe and Stouffer. Thus, there is some but not general model agreement as to summer drying in middle and high latitudes. Furthermore, all the models suggest significant high-latitude increases in precipitation, and hence runoff.

Figure 5.18 Same as Figure 5.17, except longitudinal average values of soil moisture in cm plotted versus month

Figure 5.19 Changes in soil moisture content in mm for the June to August period for 4 x CO₂ according to Mitchell and Lupton (1984)

5.7.2 Exploratory GCMs

 It is difficult to judge the validity of the climatic change given by the more detailed GCMs unless it is possible to interpret their results in terms of well understood physical processes. Such interpretation is not readily developed using only the more realistic models both because of limitations in computer time and because of the inherent complexity of these models. Thus, it is necessary to study the climatic change question with a hierarchy of simpler models (Schneider and Dickinson, 1974) including simple GCMs.

Manabe and co-workers have developed a model consisting of 120^° of longitude, half flat land and half ocean, and have used this sector model for a number of interesting studies; e.g., Wetherald and Manabe (1980) studied the role of interactive cloudiness in climatic change, and Manabe and Wetherald (1980) studied the differences between annual mean and seasonal cycle simulations. It is not possible to further summarize here the results from these or several other interesting studies from other groups.

Simulations involving coupling of a sector GCM to an ocean model have been discussed by Bryan et al. (1982) and Spelman and Manabe (1984). It is usually easier to analyse and interpret the results from a sector model than those from a global model because of the simplicity of the geography of the sector model. With an impulsive change in CO₂ global heating, Bryan et al. found (Figure 5.20) that after 25 years their model surface temperatures had nearly the same latitudinal distribution as a steady-state calculation and about 0.7 the amplitude of the steady-state response. Thompson and Schneider (1982) have argued that Bryan et al. could have come to a different conclusion if their high-latitude ocean had a larger heat capacity as appropriate to the Southern Hemisphere. Figure 5.21 shows the vertical distribution for the Bryan et al. model of the ratio of transient to steady-state temperature increase. Evidently, temperature increase in the ocean is largely confined to the upper 300 metres. The increased stable stratification of the upper layers of the ocean and thermal insulation by sea ice help to reduce the large effective thermal inertia of high latitudes.

Spelman and Manabe (1984) found a much smaller temperature increase for quadrupling of CO₂ using their ocean GCM which simulates poleward transport of heat by ocean currents than they found with an otherwise similar mixed-layer model. Through further integrations, they discovered that this difference could be associated with differences in global average control temperature as shown in Figure 5.22. This dependence on global mean temperature is presumably a result of differences in ice-albedo feedbacks, e.g., as discussed in Schneider and Dickinson (1974).

Washington and Meehl (1983) studied the climatic change from CO₂ doubling using an annual mean swamp model with realistic geography. Their calculation had essentially no ice-albedo feedback and no indication of high-altitude intensification of the temperature increase. Their global average warming of 1.3 ° is the smallest warming obtained by any GCM for doubling CO₂ simulations and only one-third the global warming obtained using a seasonal version of essentially the same model, i.e., Washington and Meehl (1984). They suggest that this small response is due to weak ice-albedo and water vapour feedback. Their model indeed appears to have essentially no albedo feedback, which they interpret to result in part from their control simulation having a mean surface air temperature 1.7 °C warmer than that of their seasonal cycle model and in part from weak water vapour feedback. There does not appear, however, to be anything anomalous in their water vapour feedback, as both models have `maximum increases of moisture' in the lower troposphere of 0.57 g kg^-1 per °C of warming. Thus, why their warming was significantly less than the usual 2 °C warming of radiative convective models is not known. Their weak warming could have involved negative feedbacks from lapse rate, water vapour profile or cloud changes.

Figure 5.20 Timelatitude variation of the zonally averaged normalized response in ^°C of (a) sea surface air temperature and (b) surface air temperature averaged over continent and ocean for an instantaneous 4 x increase of CO₂ (Bryan et al,. 1982)

Figure 5.21 Latitudeheight distributions from the transient response study for instantaneous 4 x CO₂ showing (a) the zonally averaged temperature at 25 years minus intitial temperature (°C) and (b) the fractional response of zonally averaged temperature relative to steady state (from Spelman and Manabe, 1984)

Figure 5.22 The change of global mean surface air temperature (°C) in various GFDL models for 4 x CO₂ 1 x CO₂ versus global mean control temperatures. Solid dots are plotted for the models having limited computational domain with idealized geography; the triangle indicates the model that has global domain with realistic geography. From Spelman and Manabe (1984)

5.8 RELIABILITY OF MODEL RESULTS

5.8.1 Global Mean

The scenarios presented in Chapter 3 suggest that it is unlikely that the atmospheric CO₂ concentration will double before 2050, while a modest increase of CO₂ emissions would lead to about a doubling of the concentration towards the end of the next century. Since, furthermore, increased atmospheric heating grows logarithmically with CO₂ concentration, the climate around the year 2100 could be near-equilibrium with the CO₂ concentration present at that time. I shall now argue that the global average equilibrium warming for doubled CO₂ would lie between 1.5 and 5.5 °C and probably between 2.5 and 4.5 ^°C. The largest known sources of uncertainty from the modelling viewpoint are the feedbacks due to ice albedo and cloud radiative properties. Recent studies, including those reviewed here, have suggested that these terms may either provide large positive feedback to forced climatic change or alternatively give very little feedback. A significant negative feedback for clouds has also not been excluded. In the present assessment of uncertainty, the confidence limits have been broadened from those previously arrived at by the Climate Research Board (1979) of 3 ± 1.5 °C. Two GCM studies have been recently published with global temperature increase in the upper range of the Climate Research Board's stated confidence limits (i.e., Washington and Meehl, 1984; Hansen et al., 1984), but with different large positive feedbacks primarily responsible for their large estimates. Evidently, we cannot exclude the possibility of both large ice-albedo and large cloud feedbacks occurring together. Furthermore, Washington and Meehl (1983) found a temperature increase for doubled CO₂ of 1.3 °C which is below the Climate Research Board's lower limit of 1.5 °C.

One formal procedure to evaluate the uncertainty in global warming is to estimate the uncertainty in the feedback factor in Eq. (5.1). The different contributions to are assumed to be independent stochastic variables with normal distribution about some expected value. We could attempt to approach the uncertainty analysis mechanically by viewing different GCM simulations as providing samples from the ensemble of possible climates. However, I believe that in this situation a more satisfactory approach is a Bayesian one, that is, using all the available information, including also judgmental estimation to obtain expected values and standard deviations.

A standard value for from one-dimensional radiative convective models, in the absence of ice and cloud feedback with fixed cloud top altitude and fixed relative humidity, is 2.0 W m^-2 °C^-1 (Ramanathan and Coakley, 1978). To this must be added an icealbedo feedback term which is estimated to be 0.4 ± 0.3 W m² °C^-1 based on previous GCM model simulations, empirical estimates, and the current status of sea-ice modelling capabilities. The confidence limits are intended to refer to two standard deviations. The following information has been considered in arriving at this judgmental estimate. Estimates of this term inferred from different studies are Washington and Meehl (1983), 0.1 W m^-2 °C^-1; Lian and Cess (1977) using a seasonal energy balance model with a snowice parameterization based on seasonal variation of satellite-measured albedo, 0.3 W m^-2 °C^-1; Hansen et al. (1984), 0.3 and 0.4 W m^{-2 °}C^-1;Robock (1983a) from measured seasonal variation of snow and ice cover, 0.6 W m^-2 °C^-1; Manabe and Stouffer (1980), 0.3 W m^-2 °C^-1; Wetherald and Manabe (1981), 0.4 to 0.5 W m^-2 °C^-1; Spelman and Manabe (1984), 0.45 W m^-2 °C^-1; Washington and Meehl (1984), -0.6 W m^{-2 °}C^-1.The ice-albedo feedback in the Manabe and Stouffer model is probably too low because of too little sea ice in the Antarctic and model snowice albedos that may be too low, whereas the icealbedo feedback of Washington and Meehl (1984) is probably too high because of excessive sea ice and too high albedo for summer pack ice in their control in both hemispheres. However, it might also be argued that the latter study could conceivably have too weak an icealbedo feedback because of the weakness of its seasonal cycle response to annual forcing. Without further analysis, neither of these two studies can be regarded as much beyond a standard deviation of a best value. Since about 80% of the WashingtonMeehl icealbedo feedback is in the Southern Hemisphere and about 80% of the Manabe Stouffer icealbedo feedback is in the Northern Hemisphere, an icealbedo term between -0.2 and -0.7 can be obtained by using one hemisphere from one model and another hemisphere from the other model. The Washington and Meehl (1983) result is taken to be two standard deviations on the low side because of lack of any plausible physical mechanism to provide so little icealbedo feedback. One large source of uncertainty in modelling the sea-ice-albedo feedback is the amount and thickness of clouds covering the sea ice and their possible change with changed sea-ice cover. The icealbedo feedback of Hansen et al. (1984) appears to have been strongly masked by high-latitude cloudiness which increased with CO₂ warming.

The second serious source of uncertainty in the question of global climatic change is that of cloud feedback. The Hansen et al. model estimates this parameter to be 0.8 W m^-2 °C^-1 (i.e., positive feedback), whereas Manabe and Wetherald (1980) find it for annual mean model to be only 0.05 W m^{-2 °}C^-1 as a result of cancellation of positive feedback in low latitudes and negative feedback from stratus clouds in high latitudes. The study by Washington and Meehl (1984) shows cloud changes qualitatively similar to those of Hansen et al. but weaker. Their cloud feedback is estimated to be about 0.3 W m^-2 °C^-1. Cess et al. (1982) provide another estimate of 0.0. Formally combining these four estimates gives a mean of 0.3 and a standard deviation of 0.35, which doubled gives 0.7 as an `error bar'. None of the above three-dimensional studies has considered the probable negative feedback from increasing cloud liquid water with a warmer climate. Hansen et al. examined the effect of cloud optical thickness change with a one-dimensional radiative convective model and found it could cancel all the positive feedback found in their three-dimensional model. Other one-dimensional studies have also demonstrated the possibility of large negative feedbacks from cloud optical thickness change (e.g., Somerville and Rener, 1984, and references therein). We take as a judgmental estimate 0.3 ± 0.7 W m^{-2 °}C^-1 for the cloud feedback contribution to (the same as obtained by formally combining model results above).

We estimate the contribution of all other feedbacks, e.g., from changes in lapse rate, vertical distribution of humidity, horizontal transport by atmosphere and oceans to be 0.0 ± 0.4 W m^{-2 °}C^-1. The analysis of Hansen et al. found lapse rate and humidity vertical distribution feedbacks to be individually large but mostly cancelling.

The estimated means for various feedbacks as discussed above are linearly averaged and the error bars are root-mean-square-averaged to give = 1.3 ± 0.86 W m^{-2 °}C^-1.The confidence limits of 0.45 to 2.16 W m^{-2 °}C^-1are divided into 4.2 W m^-2 for CO₂ doubling to give a range of temperature increase of from 2.0 to 9 °C. Such a large change as the upper limit just obtained cannot be excluded, but I believe it to be extremely unlikely. Given the range of past climate variations, the present weak evidence for global warming (as discussed in Chapter 6), and the questionableness of the present analysis for such large changes, a more reasonable upper limit is believed to be 5.5 °C. The largest GCM warming yet reported for doubling CO₂ is 4.8 °C obtained by Hansen et al., for their alternative control with more sea ice. I have also judgmentally dropped the lower limit to 1.5 ^°C in recognition of the 1.3 ^°C temperature increase obtained by Washington and Meehl (1983). A best estimate of temperature response is proportional to the expected value of 1/ which cannot be obtained directly from the expected value of . Assuming that has a Gaussian distribution with mean of 1.3 and standard deviation of 0.43 but truncated to exclude values less than 0.3, I find that = 1.14 (where the bars refer to expected values). Roughly speaking the possibility of small values of becomes weighted more heavily when we invert . Thus, the expected temperature change is 4.2 x 1.14/1.3 = 3.7 °C. In round numbers, the estimated T for steady-state CO₂ doubling is 3.5 ± 2 °C.

It is evident that the above discussion, although couched in terms of a zero-dimensional climate model, obtains most of its quantitative information from GCM studies. Only by narrowing the uncertainties and errors in the GCM simulations can we hope to improve significantly our estimates of future climatic change. Values of warming for equilibrium CO₂ doubling greater than 4 °C are suggested by two recently published studies and by some GCM studies yet unpublished (and so not reviewed here) which were not available to previous assessments. These studies indicate that either large positive cloud feedbacks or, alternatively, large icealbedo feedbacks and modest positive cloud feedbacks can give warmings of at least 4 °C. The possibility cannot be excluded that both large positive cloud feedback and large icealbedo feedback might be realized. For example, the Hansen et al. (1984) simulations but with an icealbedo feedback as strong as that of Washington and Meehl (1984) would give a 6 °C warming. Icealbedo feedback necessarily weakens with a warmer climate and would become much weaker with the disappearance of polar sea ice during the summer. Likewise, cloud feedbacks would greatly weaken with the near disappearance of cloud cover. However, disappearance of summer sea ice and large reductions in cloudiness would increase absorbed solar radiation by at least several tens of W m^-2.

Weak cloud feedbacks and relatively small icealbedo feedbacks are also not unlikely and together would imply CO₂ doubling temperature changes in the range 2 to 3 °C. While the assumption of a statistical model for the distribution of feedback factors is not justified by any real information we have for the feedback terms, it provides guidance for the combination of uncertainties and suggests that the possibility of a relatively small total feedback should be given somewhat more weight than the possibility of a relatively large total feedback. In summary, the CO₂ doubling equilibrium warming is likely (estimated probability of 68%) to be in the range 2.5 to 4.5 °C with only a small possibility, judged to have a 5% probability, for values to lie outside this range by more than 1 °C. A warming of as little as 1 °C or as large as 7 °C cannot be entirely excluded from the modelling evidence for CO₂ doubling but would seem extremely unlikely.

To estimate the temperature increase at a given date requires scaling the above estimates to the expected CO₂ concentrations at that date, adding an estimate of the net warming from increases of other anthropogenic gases, and combining the above uncertainties with the uncertainties in the concentrations of CO₂ and other trace gas increases expected by that date. In addition, for rapid growth of heating as at present, a further correction is needed for the effects of ocean heat storage.

The increase of global rainfall is likely to scale like the increase of saturation vapour pressure and thus follow global temperature change but weighted toward the temperature change in moist tropical regions where evapotranspiration is normally largest.

5.8.2 Consideration of Transient Lag Due to Ocean Heat Uptake

Most GCM studies have concentrated on the equilibrium response to doubling or quadrupling CO₂. The heating by other trace gases can be expressed in terms of equivalent concentrations of CO₂. The present-day equilibrium response is about one-third of that which would correspond to a doubling of CO₂. As evident from Eq. (5.1), we must in general consider also the effect of the time-dependent ocean heat storage, that is, the rate of heat taken up by the oceans. This term might become sufficiently small in a century or two to be negligible. However, as a result of the rapid growth in fossil fuel emissions over the recent past, the ocean heat uptake term is of comparable magnitude to the net feedback term that has been extensively discussed in this chapter. Under these conditions, it is evident from Eq. (5.1) that the warming now resulting from the past increases of CO₂ should vary more weakly with than as 1/, as pointed out by Hansen et al. (1984). Indeed, in the limit of very rapid growth of the heat input, almost all the heating would go into the ocean and the temperature change would be nearly independent of as seen analytically, e.g., if an exponential growth of Q is assumed with an exponent large compared to /C.

A family of more realistic zero-dimensional transient models with a surface mixed layer coupled to an underlying diffusive ocean has been analysed by Wigley and Schlesinger (1985). For a plausible range of parameters, they show that an increase of CO₂ from 270 ppmv to current values of 340 ppmv implies the present warming to lie between about 0.3 and at least 0.8 °C, assuming that the steady-state doubling response lies between 1.5 and 4.5 °C. The warming from other trace gases was estimated to be an additional 0.2 °C, but this would be offset if the initial CO₂ level were raised to 290 ppmv. Hansen et al. (1984) earlier found similar results. Wigley et al. (Chapter 6) suggest that the transient warming to date due to CO₂ and other trace gas changes should be in the range 0.31.1 ^°C, given all model uncertainties. Harvey (1985) has discussed parameterization changes that can modify the time scale of the calculated transient ocean temperature response to CO₂ warming. Particularly important seems to be whether energy imbalances over land are compensated locally or are coupled to ocean temperature changes. He also emphasizes the possible effect of including vertical advection which, for fixed eddy diffusion, shortens the response time. However, with inclusion of vertical advection, it is presumably necessary to increase eddy diffusion coefficients to maintain agreement with tracer data and such an adjustment would lessen the response time change.

The detailed mechanisms of ocean heat uptake are poorly known, especially in regions of deep and bottom water formation so that the ratio of actual to steady-state warming could be more uncertain than indicated by the analyses of Hansen et al., Wigley and Schlesinger, and Harvey.

5.8.3 Regional Patterns

Only the global average temperature change can be constrained by physical arguments such as given above. Thus, any changes in regional patterns of climate are much more speculative. Several possible features of regional climatic change have been suggested. First, there is the indication that warming will be enhanced in high latitudes. All the models discussed here appear to agree qualitatively with the hypothesis of Manabe and Stouffer (1980) that large wintertime warming would be expected over polar sea ice. However, the extent of sea-ice recession is quite uncertain for the reasons discussed earlier. Another plausible result, reported in models of Manabe and co-workers and Mitchell and co-workers but not in the other models discussed, is a preponderance of summertime soil moisture decrease in middle and high latitudes of the Northern Hemisphere. High latitude precipitation increases in all the models.

5.8.4 Model Results as a Guide to Detecting CO₂ Climatic Change Over the Next Few Decades

As discussed above and in Chapter 6, allowance for ocean heat uptake indicates that the present CO₂ warming signal should lie approximately between 0.3 and 1.1 °C. None of the GCM model results for regional pattern is yet sufficiently certain as to suggest useful regional `fingerprints' for the warming signal. Thus, as discussed further in the next chapter, global average temperature is the most useful quantity to monitor. This term should show an increase with time following, with some time lag, the logarithm of the atmospheric CO₂ concentration. Because of the considerable uncertainty in the expected CO₂ signal, a temperature increase of about 1 °C or larger maintained over at least a decade may be required to provide convincing evidence of the long-awaited CO₂ temperature increase. If means were found not only to identify but also to monitor some of the causes of natural variability such as volcanic aerosol, the task of obtaining evidence of the CO₂ signal would be made easier.

5.9 CONCLUSIONS

• Results are now available from several independent GCM modelling groups which all show a warming of at least several degrees for the climate response to doubling the atmospheric concentrations of CO₂.

• The global equilibrium temperature change expected from increases of CO₂ and other trace gases equivalent to a doubling of CO₂ is expected to be in the range 1.5 to 5.5°.

• The largest sources of uncertainty in modelling global average temperature change appear to be the level of feedback from clouds, icealbedo, and possibly lapse-rate and water-vapour changes.

• Storage of heat in the oceans reduces the warming presently expected for an equilibrium response to carbon dioxide heating (and that of other trace gases) and may significantly modify the geographical distribution of climatic change.

• The global warming in 1985 suggested by models to result from previous increases of CO₂ and other trace gases is in the range of 0.3 to 1.1 °C.

• Continental-scale climatic change, especially that involving conditions required for agriculture, is extremely important but not yet modelled with any degree of confidence. There is qualitative agreement among all current three-dimensional models that largest equilibrium temperature increases would occur in regions of high-latitude winter. There is some but not compelling evidence for mid-latitude mid-continent summer drying. High-latitude precipitation increases in winter are likely.

• Recommendations:

1. The modelling of cloud radiative interactions and icesnow albedo in GCMs as used to model future climatic change needs to be significantly improved using better physical parameterizations and based on current and future data sets.

2. Model simulations of climatic change from increases of CO₂ are most readily interpreted in terms of global feedback factors. Future model studies should attempt to explicitly obtain the feedback effects of cloud property changes, ice-albedo feedback, and lapse-rate feedbacks.

3. More generally, modellers should attempt to present the most important model results in as uniform a graphical and numerical format as possible.

ACKNOWLEDGEMENTS

Part of Section 5.1 and most of Section 5.2 were originally drafted by Tom Wigley. Helpful suggestions to improve the manuscript were given on the initial draft by James Hansen, Brian Hanson, Gerald Meehl, Alan Robock, and Warren Washington. Further extensive suggestions were given by the International Meteorological Institute review committee: Georgi Golitsyn, Eero Holopainen, Syukuro Manabe, John Mitchell, and David Parker. On a later draft valuable comments were provided by Stephen Schneider.

The author also wishes to acknowledge comments made by T. Asai, A. Berger, W. Böhme, H. W. Ellsaesser, H. L. Ferguson, R. M. Gifford, J. Goudriaan, H. Landsberg, J. A. Laurmann, G. McBean, F. Mesinger, A. S. Monin, O. Preining, R. W. Stewart, J. Tukey, J. Woods, and Du-Zheng Ye.

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