15.2 Radiation in the Atmosphere

15.2.1 Solar Radiation

Solar radiation is the primary source of energy for the Earth system. This energy is provided mostly in the form of ultraviolet, visible, and near-infrared radiation (wavelength between 0.2 and 4 µm). At the top of the atmosphere, the shortwave energy flux intercepted by a surface normal to the direction of the Sun is approximately equal to 1370 W m^-2, and is called the solar constant. The corresponding energy captured by the Earth's system is on the average 342 W m^-2. This energy is mainly absorbed in the atmosphere by molecular oxygen (O₂), ozone (O₃), and water vapor (H₂O), as described in Chapter 3. The absorption of solar radiation by ozone provides the energy that heats the stratosphere and mesosphere (see Chapter 2). The portion of solar radiation that is not absorbed in the atmosphere or backscattered to space reaches the Earth's surface. Figure 15.1 presents the spectrum of solar radiation outside the Earth's atmosphere and at sea level for clear sky conditions. Since the troposphere and the surface are coupled by convective exchanges, this energy almost simultaneously heats the soil, the vegetation, and the oceans as well as the entire troposphere, except in cases of temperature inversions near the surface (temperature increasing with height).

The intensity of radiation emitted by the Sun is not entirely constant as a function of time. For example, variations in the "solar constant" of approximately a tenth of a percent are observed and linked to the 11-year solar cycle. Several attempts have been made to correlate the past evolution of climate with solar activity, but the subject remains controversial, since there are no reliable measurements of solar constant changes before the mid-1970s, and very little change has occurred since then.

15.2.2 Terrestrial Radiation

The energy provided by the Sun and absorbed by the Earth is reradiated as infrared radiation (see Box 15.2). This energy is absorbed by clouds as well as atmospheric molecules, the major absorbers being water vapor and carbon dioxide; these two gases are sufficiently abundant to trap a large fraction of the energy (mostly in the 12 to 20 µm spectral region) in the lowest layers of the atmosphere. In the 8 to 12 µm region, called the atmospheric window, terrestrial radiation propagates to space because of the relatively weak absorption in this region of the spectrum. Therefore, any gas with strong absorption properties in this spectral region is expected to be relatively efficient in trapping terrestrial radiation. The spectral locations of the absorption features of the main greenhouse gases in the atmospheric window are shown in Figure 15.2. An example of a terrestrial radiation spectrum measured at the top of the atmosphere by the Nimbus-3 IRIS instrument is shown in Figure 15.3. The absorbing bands such as the 9.6 µm band of O₃ and the 15 µm band of CO₂, as well as the atmospheric window and several other features (H₂O, CH₄), are noticeable. These radiatively active gases, also called greenhouse gases, absorb only a small fraction of solar energy, but they are very effective in absorbing as well as emitting longwave radiation. Their net effect is to reduce the amount of radiative energy emitted to space and to increase the radiative energy provided to the surface-troposphere system. The fundamental reason for the existence of the "greenhouse effect" is that the temperature decreases with altitude in the troposphere. Radiatively active gases as well as clouds absorb the radiation emitted by the warmer surface, while their emission of radiation to space occurs at colder atmospheric temperatures. The trapping of the radiation by radiatively active molecules produces an increase in the surface temperature of about 33 degrees Celsius (assuming no change in albedo when atmosphere is removed). Without the "greenhouse effect" the average temperature at the surface would be only -18°C and life would not be possible on Earth. At higher altitudes, the radiative emission to space in the 15 µm band of CO₂ contributes to a cooling in the stratosphere and mesosphere.

Surface climates are directly influenced by the radiation balance between incoming solar radiation and outgoing (reflected solar + infrared) radiation. A global energy budget of the Earth system can be approximately described as follows (Fig. 15.4): The solar energy penetrating into the Earth's system represents about 342 W m^-2, of which about 107 W m^-2 (or 31%) is returned to space (24% due to backscattering by clouds, air molecules, and particles, and 7% due to reflection at the Earth's surface), 87 W m^-2 (or 25%) is absorbed within the atmosphere, by ozone in the stratosphere, and by clouds and water in the troposphere. The remaining 148 W m^-2 (or 43%) is absorbed at the Earth's surface. From the terrestrial energy emitted by the surface (390 W m^-2 or 114%), only 40 W m^-2 (12% of the incoming solar radiation) escapes directly to space in the atmospheric window. The remaining 310 W m^-2 (or 90%) is absorbed within the troposphere by water vapor, CO₂, O₃, and the other greenhouse gases, as well as by clouds and aerosols. Finally, an energy of about 335 W m^-2 (or 98%) is emitted back to the surface, while 195 W m^-2 (or 57%) is emitted to space. The excess energy received by the surface is compensated by nonradiative processes such as evaporation (latent heat flux of 78 W m^-2, or 23%) and turbulence (sensible heat flux of 15 W m^-2, or 4%).

Note the difference between the radiative emission at the Earth's surface (390 W m^-2) and the total infrared emission to space (40 + 195 = 235 W m^-2). This energy trapped in the atmosphere (155 W m^-2) represents the greenhouse effect. With the exception of numbers given for the top of the atmosphere, these values are uncertain by approximately 10 to 20%.

Among the gases present in the atmosphere, the largest contribution to the greenhouse effect is provided by water vapor, followed by CO₂ and other trace gases such as CH₄, N₂O, O₃, CFCs, HCFCs, and HFCs.

Clouds also absorb and emit infrared radiation. In addition, they increase the planetary albedo (defined as the fraction of the incoming radiation that is reflected). Their net effect on the climate system is complex. It is believed that high-altitude cirrus clouds contribute to warming, while low-level stratus clouds contribute to cooling. Overall, the presence of clouds tends to cool the Earth's system. However, complex feedback effects could lead to warming or cooling effects, depending on specific cloud changes in response to changes in climate forcing.

As the concentration of several radiatively active gases are increasing as a result of human activities, there is great concern about a possible increase in the greenhouse forcing. When the concentration of a radiatively active gas increases, initially the longwave radiation to space is reduced. As a result, the energy budget is out of balance at the top of the atmosphere. At the same time, if this gas does not affect the absorption of solar radiation, the net radiative energy available in the lower atmosphere and at the Earth's surface increases and the energy balance is restored through a warming of the surface-troposphere system.

15.3 Natural Variations: Past Climates

One of the most fascinating confirmations of a link between atmospheric trace gas concentrations and climate is provided by the data obtained from ice cores collected in polar regions. Figure 15.5 shows the correlations between atmospheric trace gas content and temperature over the past 240,000 years. Clearly (assuming that the Vostok temperature series is representative of the global mean temperature), when the atmospheric abundances of CO₂ and CH₄ are low, the Earth is in a relatively cool climate state. To first order, when greenhouse gases are in relatively low abundance in the atmosphere, there is less infrared trapping of heat and the Earth surface is cool, perhaps cool enough to initiate glaciation. However, it should be noted that it is not clear if CO₂ was lower before or after the cooling occurred. Phase shifting of the temperature changes and atmospheric CH₄ and CO₂ concentrations is evident in some data sets. It is not straightforward to assign cause and effect relationships based on these time lags due to possible amplification effects (feedback mechanisms in the Earth system). Changes in surface temperatures and the areas covered by ice sheet have undoubtedly affected the exchange rates of greenhouse gases between the surface (continents, oceans) and the atmosphere. Simultaneously, the atmospheric abundance of these gases has affected the Earth's climate.

15.4 Impact of Anthropogenic Trace Gases on Climate

Although water vapor is the most important greenhouse gas, its distribution in the atmosphere is mainly driven by physical processes, but is only slightly affected by human activities (e.g., deforestation on a large scale, which can matter regionally). Human activities are, however, responsible for significant changes in the abundance of other radiative gases, as seen in previous chapters.

Table 15.1 provides an estimate of the greenhouse gas concentrations and trends; the origin and magnitude of these trends are further discussed in Chapters 5, 8, and 9.

Changes in the distributions of the trace gases are expected to affect the climate system through spatial and temporal changes in the flux of radiative energy into and out of the surface-troposphere system. This impact can, in principle, be quantified by calculating the induced change in the surface temperature; however, this quantity is largely dependent on complex feedback processes, which are not fully understood nor easily represented or verified in existing climate models. It is more straightforward to calculate the radiative forcing. This quantity is defined as the response in the net radiative energy flux at the tropopause to changes in the concentration of a given trace gas. Several factors determine the ability of an atmospheric gas to affect the radiative forcing: its atmospheric concentration, the strength and spectral position of its absorption bands, temperature, and pressure.

The radiative forcing associated with changes in the abundance of trace gases can be estimated by radiative models. The solution of the radiative transfer equations is complex since the absorption spectra of atmospheric molecules exhibit structures characterizing their numerous rotation and vibration-rotation lines (see Box 15.2). The absorption by these molecules varies considerably over small wavelength regions, and exact calculations require line-by-line integrations. However, such calculations require very large amounts of computer time. This direct approach is usually replaced by an approximate method in which the line or band characteristics are expressed in terms of global parameters. Radiative models have been developed to treat either sections of bands (narrow-band model) or entire bands (wide-band models) (Tiwari, 1978). The radiative codes included in multidimensional models (2D and 3D) use generally one of these two approaches.

15.4.1 Direct Radiative Effects

CH₄, O₃, N₂O, CFC-11, CFC-12, and various CFCs and HCFCs have strong absorption bands in the atmospheric window region. These trace gases absorb and emit radiation in bands composed of discrete lines with extended wings. For gases that are present in small quantities, such as the CFCs and HCFCs, the absorption increases quasilinearly with their atmospheric concentration. However, for gases with larger concentrations, such as methane and nitrous oxide, the absorption at the center of the bands is already saturated for present atmospheric abundances, and increasing absorption with increasing concentrations occurs mainly in the wings of the lines. In this case the radiative forcing is approximately proportional to the square root of the concentration change. For the most abundant radiatively active species such as CO₂, the atmosphere is almost entirely opaque in the center of the absorption lines, and the radiative effect of adding CO₂ is only noticeable in the wings of the lines. In this case, the absorption can be approximated by a logarithmic relationship with the CO₂ concentration. A doubling in the atmospheric abundance of CO₂ leads to an increase in the radiative forcing of about 4.6 W m^-2.

Simplified expressions providing the direct radiative forcing as a function of the greenhouse gases concentrations are given in Table 15.2 for both clear sky and average cloudiness conditions. These formulas are only approximate and should be applied only for small changes in the concentrations.

A useful index also used to evaluate the radiative impact of increasing greenhouse gases concentrations is provided by the relative radiative forcing. This index provides a direct comparison between the direct radiative forcing of a greenhouse gas and that of CO₂ (chosen here as the reference molecule). Values of the direct relative radiative forcing for several greenhouse gases are given in Table 15.3 for a 1990 reference atmosphere, for both clear sky and cloudy conditions, calculated for a 10% increase in the concentrations of the more abundant greenhouse gases. It should be emphasized that since radiative fluxes do not change linearly with the concentrations of trace gases, the calculated relative radiative forcing depends on the background concentrations for the greenhouse gases, as well as the magnitude of the changes applied to these concentrations. As an example, the relative forcing of methane as compared to CO₂ would be 24.4 for an increase of 1% in the concentrations of both CO₂ and CH₄, while it would be 27.6 for a doubling in the concentrations of both CH₄ and CO₂.

15.4.2 Indirect Effects: Chemical Feedbacks

Many climate models including general circulation models (GCMs), which are used to predict climate changes, use CO₂ as a proxy for other greenhouse gases and often estimate climate changes for a doubling in the equivalent CO₂ concentrations. Most of them currently do not explicitly account for the greenhouse effect of other trace gases. The use of a CO₂ proxy to represent the combined greenhouse forcing of CO₂ and the other radiatively active trace gases is questionable due to the differences in the spectral and chemical properties of all gases involved. For example, Figure 15.6 shows the difference in the heating rate calculated for a doubling of the CO₂ concentration (Fig. 15.6a) and an explicit treatment of the increase in the other trace gases (Fig. 15.6b). Compared with a doubling of the CO₂ concentration, the inclusion of the radiative effect of the other trace gases results in a value of the heating rate stronger in the lower stratosphere and much lower at the surface for high latitudes.

Gases such as CH₄, N₂O, and the CFCs are not only radiatively active, but they also produce chemical perturbations in the atmosphere and hence affect the abundance of other greenhouse gases. The oxidation of methane, for example, leads to an additional production of water vapor in the stratosphere and ozone in the troposphere. The breakdown of N₂O and CFCs in the stratosphere leads to the production of active nitrogen or chlorine radicals that destroy ozone. CO₂ is chemically inactive in the atmosphere, but an increase in the CO₂ concentration and in the associated emission to space of the 15 µm radiation is expected to produce a cooling of the stratosphere and mesosphere. As the production and loss rates of ozone are strongly temperature dependent in the middle atmosphere, a CO₂ increase is expected to moderate the ozone destruction caused by chlorine and nitrogen compounds. Furthermore, a cooling of the winter polar stratosphere resulting from increasing CO₂ concentrations could lead to the formation of additional polar stratospheric clouds, which are associated with the observed dramatic destruction of ozone in the Antarctic polar stratosphere.

As a result of all these processes, stratospheric ozone could decrease globally, and more solar radiation could become available in the troposphere, leading to a warming of the surface. Less terrestrial radiation would be absorbed by ozone, leading in this case to a cooling of the surface. The net effect of stratospheric ozone changes on the climate system depends strongly on the magnitude and altitude of these changes. Moreover, all these changes could induce a modification of the circulation in the stratosphere, and thus affect the transport of other trace gases.

Human activities could also lead to an increase in the concentrations of ozone in the troposphere with potential impact (absorption of solar and terrestrial radiation) on the climate system. Such changes probably have a larger impact on the radiative forcing than those produced by ozone depletion in the stratosphere.

Increased emissions of trace gases at the Earth's surface could have a significant impact on the climate system (temperature, precipitation, frequency of extreme events), but the resulting effects are difficult to quantify because of strong non-linearities in the coupled chemical and climate systems. The available estimates of potential climate changes produced by perturbations in the chemical composition of the atmosphere are provided by interactive chemical-radiative-dynamical models.

The importance of these chemical feedbacks on the radiative forcing of the atmosphere is illustrated in Table 15.3. The indirect relative forcing of greenhouse gases has been derived by using an interactive two-dimensional model that is run to steady state. As for the calculations of the direct radiative forcing, a 1990 reference atmosphere is assumed; for each individual gas, a 10% increase in the background concentration is applied at the surface level.

Another illustration of the importance of chemical processes on the climate forcing is given in Figure 15.7. This figure represents the changes from 1900 to 1990 in the radiative forcing (1) when only considering direct radiative effects and (2) when chemical feedbacks are taken into account. The changes in the concentration of the greenhouse gases at the surface from 1900 to 1990 used in these calculations is given in Table 15.1. When chemical feedbacks are taken into account, the ozone produced as a result of the CH₄ release has a significant radiative effect, which is as strong as the direct radiative effect of methane.

15.5 Global Warming Potentials (GWPs)

The radiative forcing provides an estimate of the change in the radiative flux at the tropopause in response to changes in the concentration of greenhouse gases. In order to take into account the lifetime of the gases in the atmosphere, and hence the period of time over which the climatic effect of a perturbation in their concentration is expected to be significant, an index called the Global Warming Potential (GWP) was defined. This concept was created in order to enable decision makers to evaluate options to regulate future emissions of various greenhouse gases without having to perform complex model calculations.

The GWP of a well-mixed gas is defined (IPCC, 1990) as the time-integrated change in the radiative forcing due to the instantaneous release of 1 kg of a trace gas i expressed relative to that from the release of 1 kg of CO₂

if Delta F_R represents the change in the forcing at the tropopause and T is the time over which the integration is performed (time horizon). Using a linear approximation,

where a_i (expressed in W m^-2 kg^-1) is the instantaneous radiative forcing due to the increase in the concentration of trace gas i and nⁱ is the concentration of the gas i remaining at time t after the release (IPCC, 1990). a_CO2 and n_CO2 are the corresponding variables applied to CO₂, which is considered the reference gas. If tau_i is the lifetime of the molecule i and tau an "effective" residence time for CO₂, the GWP of the gas i can be approximated by

As indicated in the above expression, the estimation of the GWP for a trace gas requires estimates of the radiative forcing for the trace gas i and for the reference gas CO₂ per unit of mass change, the lifetimes of species i and of CO₂, and the definition of the time horizon T over which the integration is performed. The indirect chemical effects resulting from the increase in the concentration of species i also need to be evaluated.

The choice of the time horizon T depends on the type of climate impact under consideration. As each response has its own characteristic time, there is no single universally accepted value of the time horizon T that can be adopted. Table 15.4 illustrates the integration periods that are appropriate for different climatic responses.

As discussed in Chapter 5, the atmospheric abundance of CO₂ is regulated by the cycling of carbon between several biogeochemical reservoirs (atmosphere, ocean, biosphere). A single global residence time of CO₂ in the atmosphere cannot be derived. Carbon dioxide added to the atmosphere decays relatively rapidly over the first 10 years, with a more gradual decay over the next 100 years and a very slow decline over the 1000 year time scale. Expressions have been deduced from ocean-atmosphere-biosphere models that provide the decay of a perturbation in atmospheric CO₂ as a function of time. The study by Maier-Reimer and Hasselmann (1987), for example, provides an effective residence time of approximately 120 years for atmospheric CO₂. Typical global lifetimes of other trace gases are given in Table 15.5.

Table 15.5 presents a recent estimate of GWPs provided by IPCC (1995). GWPs were calculated by injecting a finite amount of trace gases to the abundance of the background atmosphere and by calculating the radiative response over several time horizons (20, 100, 500 years). The model of Siegenthaler and Joos (1992) was used to estimate the decay response of CO₂. For these calculations, the background atmospheric trace gas concentrations were held fixed (at current levels) and did not account for a possible future evolution of the atmospheric composition. Note that the decay time of a methane pulse (12-18 years) is higher than the global lifetime of this gas, since the concentration of OH decreases as CH₄ is added to the atmosphere, and the resulting GWP for CH₄ is higher than the direct GWP. The estimate of all indirect effects on the GWP (e.g., changes in ozone, water vapor, temperature, etc.) is not straightforward, and is generally model dependent.

15.6 Radiative Effects of Aerosols
15.6.1 Direct Effects

Aerosols present in the atmosphere (including sulfate particles resulting from fossil fuel combustion and elemental carbon, EC, released by biomass burning; see Color Plate 12) absorb and scatter a significant fraction of incoming solar radiation back to space. The addition of anthropogenic (not EC) and volcanic aerosols to the atmosphere leads therefore to a reduction in the net radiation available at the surface and so to a cooling of the Earth's system. Aerosols also absorb terrestrial radiation and thereby produce a significant heating in dense aerosol layers.

An interesting modeling study of direct forcing by sulfate aerosols and comparison with greenhouse gas forcing has been presented by Kiehl and Briegleb (1993). Best estimates from observations and modeling studies of sulfate aerosol loadings and distributions were combined with imposed lognormal aerosol distributions (as discussed in Chapter 4) and derived optical properties, and the sensitivity of their findings to these aerosol parameters were examined (Fig. 15.8). They estimate that variations in size or chemical composition would alter the estimated forcing (-0.3 W m^-2, annually averaged) by ±10%. The spatial distribution of aerosol properties may have a larger effect. This is because the greenhouse gas forcing occurs in different regions of the globe than does the anthropogenic aerosol forcing, which is strongest in the midlatitudes of the Northern Hemisphere, where most of the sources are located. In contrast, greenhouse gases, except ozone, generally become well mixed in the troposphere; their radiative effects are strongest in the region between -30° and +30° latitude. The combined effects of aerosols and greenhouse gases thus do not "cancel," but may change global temperature gradients.

It is known that organic matter can comprise a significant fraction of the tropospheric aerosol, and thus must also have a role in postulated climate effects. There is also substantial evidence that some of these species are hygroscopic and thus should contribute to indirect climate effects as well (Novakov and Penner, 1993). Soot has been detected in all regions of the globe, even in "remote" areas. Its strong solar radiation absorption characteristics suggest that climate forcing due to suspended soot aerosol will have a sign opposite that of sulfate. The net radiative forcing of a mixture of sulfate and soot could therefore be substantially smaller than the forcing calculated for sulfate only.

Widespread dust plumes are often detected in satellite images, and it might be expected that dust contributes to aerosol radiative forcing. Mineral dust aerosol may both scatter and absorb solar radiation, depending upon its composition and the wavelength of light considered. Sokolik et al. (1993) compared measurements of the complex refractive index for atmospheric dust aerosols and showed that the large range of values for the imaginary part of the refractive index leads to significant differences in estimates of radiative forcing. The uncertainty is magnified when one considers the effects of the presence of other suspended material (e.g., soot). Rather than dust inducing a significant effect on climate, the major impacts may follow in the opposite direction; that is, climate change may significantly affect dust production and transport. Changes in aridity in North Africa and shifts in large-scale atmospheric circulation patterns associated with climate change may alter the magnitude and pattern of Saharan dust transport to the North Atlantic (Arimoto et al., 1992).

Large volcanic eruptions, such as those of El Chichón (1982) and Mt. Pinatubo (1991), have substantially enhanced the aerosol load of the atmosphere for a few years, resulting in a noticeable cooling of the surface. One year after the eruption of Mt. Pinatubo the radiation forcing was estimated to have been -4 W m^-2 while an anomaly of -0.3 to -0.4°C in the global temperature was reported (Dutton and Christy, 1992; IPCC, 1995). Such volcanic perturbations are, however, transitory, with a typical time constant of 1-2 years.

The radiative forcing produced by the enhanced anthropogenic sulfate aerosol burden since preindustrial times is estimated (on the global scale) to be approximately -0.6±0.3 W m^-2 (IPCC, 1995). Because of their relatively limited lifetime (a few days), anthropogenic aerosols are mostly concentrated in industrialized regions (eastern United States, Europe, eastern Asia), where their radiative impact is believed to be significant. Although on the global scale their radiative impact is considerably smaller than the forcing caused by anthropogenic greenhouse gases (approximately 2.5 W m^-2), in industrialized areas the cooling caused by aerosols exceeds the warming produced by enhanced CO₂ and other radiatively active gases (Fig. 15.9).

Sulfate aerosols also serve as cloud condensation nuclei (CCN) and hence affect the formation and the radiative properties of clouds. This indirect climate impact of anthropogenic sulfur remains poorly quantified, but could be as large as or even larger than the direct forcing by aerosols of human origin.

An understanding of the role of aerosol mixtures in the past and for the present day, and extensions to predict climate change, is hindered by large uncertainties in many key quantities needed for such estimates. Quantification of major uncertainties and a proposal for strategies for minimizing them are presented in the review by Penner et al. (1993) (Table 15.6).

15.6.2 Indirect Effects

The subset of atmospheric aerosols active as CCN may have an "indirect effect" on climate by altering the albedo of clouds. Changes in the availability of CCN may change nucleated droplet number concentrations. As droplet number concentrations increase for fixed liquid water content, the mean droplet size decreases and the reflectivity of the cloud increases; the global energy balance is sensitive to such changes. Studies of potential "indirect" aerosol effects have focused upon the role of marine stratocumulus clouds, in part because of their ubiquity (they cover about 25% of the Earth's surface) and because the potential for perturbations to these clouds is high. Marine clouds generally have low droplet concentrations (on the order of 100 cm^-3), believed to be limited by the availability of CCN. Any process, then, that alters the relative amounts of CCN in marine regions may affect the albedo of these clouds. In contrast, clouds formed over continental regions are believed to have an excess of CCN available, and the number activated is most likely related to other factors such as the maximum supersaturation. However, there is observational evidence for a dependence of continental cloud drop concentration on aerosol loading (e.g., Leaitch et al., 1992). Han et al. (1994) derived effective cloud drop radii from satellite data and reported systematic differences in drop size between continental and marine water clouds and between marine clouds in the Northern and in the Southern Hemispheres. Smaller drop radii were found in those regions most affected by anthropogenic pollution, in support of the "indirect effect" hypothesis.

The importance of sulfate to aerosol and CCN concentrations led to the interesting hypothesis of Charlson et al. (1987) of a climate feedback loop involving marine phytoplankton, DMS emissions, CCN concentrations, and cloud radiative forcing. This work spurred much of the subsequent research and debate regarding indirect climate effects of aerosols. Some estimates suggest that a 30% change in CCN available to marine stratus will lead to a globally averaged forcing of 1 W m^-2. However, changes in CCN populations may have other effects that also influence climate. For example, enhanced droplet concentrations may reduce the likelihood of precipitation from clouds, altering cloud cover and cloud lifetime (Radke et al., 1989). The response of cloud liquid water content to changes in CCN and climate is not well understood. Changes in precipitation would also change the atmospheric concentration of the most important greenhouse gas: water vapor.

Climate effects of aerosols are also postulated for polar regions. The climate of polar regions is of great interest in studies of global warming. As temperatures increase the extent of snow and ice is reduced, decreasing the surface albedo and further increasing the amount of sunlight that is absorbed by the Earth-atmosphere system. Conversely, a temperature decrease will increase the surface albedo and thus reinforce the cooling (e.g., Curry et al., 1993). This feedback mechanism results in the Arctic having an impact on the global climate as well as the local climate, since the ice-albedo feedback mechanism can result in substantial modification of the net energy retained by the Earth-atmosphere system.

Several types of polar aerosol effects are postulated. Soot aerosols deposited to snow and ice surfaces may alter their albedo in a "direct" effect. An "indirect effect" for polar ice-phase clouds (present even in the lower troposphere during the coldest months of the year) may also occur via the following mechanism. Polluted air has been typically shown to be deficient in ice-forming nuclei (IN). This relationship is believed to arise from an increased sulfate mass loading in polluted air; sulfate particles, which are poor IN, coagulate with potential IN and effectively deactivate them (Borys, 1989). If this hypothesis is correct, ice nucleation in the Arctic may be relatively enhanced during winter, if there is a decrease in the oxidation of SO₂ in the relative absence of sunlight and liquid water, which could result in a decreased amount of sulfate particles. Conversely, ice nucleation during "Arctic haze" events in the Spring would be suppressed. Thus, anthropogenic aerosol has the potential to impact the amount of condensed water and the total water budget in the Arctic by modifying the ice nucleation and the phase of condensed water.

15.7 Response of the Climate System to Radiative Forcing

The simplest model to estimate the response of the Earth's climate to radiative perturbations is based on the global balance between the incoming solar energy (F_S) that is absorbed by the Earth system and the outgoing terrestrial radiative energy (F_T) that is emitted to space. For the system to be at equilibrium

If the system is perturbed by some radiative forcing Delta F_R (e.g., by an increase in the atmospheric abundance of carbon dioxide), the equilibrium between incoming and outgoing energy will be restored by a change (Delta ) in the initial fluxes (F_S and F_T), such that

Assuming that the balance is re-established by a change in surface temperature (Delta T_s), the climate sensitivity factor lambda_c, defined by

is simply given by

To make a first-order estimate of this factor, we assume that the globally averaged solar energy absorbed by the Earth system is given by

where alpha is the Earth's albedo (typically 0.3) and F₀ = 1370 W m^-2 is the solar constant (the averaged solar energy intercepted by a sphere is F₀ /4). Similarly, we assume that the terrestrial energy radiated to space is expressed by the Stefan-Boltzmann law

where sigma is the Stefan-Boltzmann constant, epsilon the emissivity of the atmosphere, and T_s the surface temperature. Assuming that alpha and epsilon are constant, and neglecting all potential feedbacks in the climate system, one derives from Eqs. (15.7-15.9) that

Under these assumptions, the value of the climate sensitivity factor is approximately equal to 0.3 K (W m^-2)^-1 (Kiehl, 1992). Thus, for a perturbation associated with a doubling in the CO₂ abundance (Delta F_R = 4.6 W m^-2), the increase Delta T_s in the mean Earth's temperature is 1.4 K, that is, significantly less than predicted by climate models or derived from satellite observations [lambda_c ~/= 0.6 K (W m^-2)^-1].

The reason for this discrepancy is that important climate feedbacks have been ignored in this simple calculation. Examples of such feedbacks include those associated with the hydrological cycle. As a result of enhanced radiative forcing, the warmer atmosphere becomes more humid (Clausius-Clapeyron relation, e.g., see Hartmann, 1994), which produces an additional greenhouse forcing and hence a larger warming of the planet. Another positive feedback is produced by changes in the surface albedo [alpha in Eq. (15.8)] when the surface area covered by ice and snow varies in response to climate change. Feedbacks caused by changes in cloudiness in response to global warming/cooling are difficult to estimate since clouds reflect solar radiation back to space (cooling effect) and, at the same time, reduce the emission to space of terrestrial radiation (warming effect). Finally, the assessment of potential feedbacks involving the biosphere remains an important research topic.

Modern climate models account for many of the relevant feedback mechanisms. When used in a predictive mode, these models attempt to simulate the transient response of the climate system to changes in the radiative forcing. This transient response is determined by the thermal inertia of the system, that is, the effective heat capacity of the atmosphere, land, and ocean, as well as the radiative damping of the system (Schneider, 1992). The response of climate to a gradual increase in the atmospheric abundance of radiatively active gases can therefore be modeled accurately only with coupled ocean-atmosphere models. A representation of a complex climate model is shown in Figure 15.10. Such models show that the existence of feedbacks associated with water vapor, clouds, and ice tends to increase the value of the lambda_c factor to a value ranging between 0.4 and 1.25 K (W m^-2)^-1 depending on the formulation in the model of the feedback processes. Thus, with these values of the feedback factor, the warming (at equilibrium) caused by a doubling in the atmospheric concentration of CO₂ should range from 1.8 to 5.8 K. The change in temperature for a CO₂ doubling, however, is not uniform in space and, as shown by Figure 15.11, is expected to be largest at high latitudes in winter. Improvements in climate predictions require, therefore, that physical, chemical, and biological processes be better understood and more accurately represented in the models.

Further Reading

Brasseur, G., ed. (1997) The Stratosphere and Its Role is the Climate System, NATO ASI Series I-54, Springer-Verlag, Berlin.

Calvert, J., ed. (1994) The Chemistry of the Atmosphere: Its Impact on Global Change, Blackwell Scientific Publications, Oxford.

Goody, R. (1995) Principles of Atmospheric Physics and Chemistry, Oxford University Press, New York.

Goody, R. M., and Y. L. Yung (1989) Atmospheric Radiation. Theoretical Basis, Oxford University Press, Oxford and New York.

Hartmann, D. L. (1994) Global Physical Climatology, Academic Press, San Diego.

Intergovernmental Panel on Climate Change, IPCC (1990) Climate Change, J. T. Houghton, G. J. Jenkins, and J. J. Ephraums, eds., Cambridge University Press, Cambridge, UK.

Intergovernmental Panel on Climate Change, IPCC (1992) Climate Change, 1992, J. T. Houghton, B. A. Callander, and S. K. Varney, eds., Cambridge University Press, Cambridge, UK.

Intergovernmental Panel on Climate Change, IPCC (1995) Climate Change: The IPCC Scientific Assessment, J. T. Houghton, L. G. Meira Filho, J. Bruce, Hoesung Lee, B. A. Callander, E. Haites, N. Harris and K. Maskell, eds., Cambridge University Press, Cambridge, UK.

Intergovernmental Panel on Climate Change, IPCC (1996) Climate Change, 1995, J. T. Houghton, L. G. Meira Filho, B. A. Callander, N. Harris, A. Kattenberg, and K. Maskell, eds., Cambridge University Press, Cambridge, UK.

Kandel, R. (1990) Our Changing Climate, McGraw Hill, New York.

Peixoto, J. P. and A. H. Oort (1992) Physics of Climate, American Institute of Physics.

Ramanathan, V., L. Callis, R. Cess, J. Hansen, I. Isaksen, W. Kuhn, A. Lacis, F. Luther, J. Mahlman, R. Reck, and M. Schlesinger (1987) Climate-chemical interactions and effects of changing atmospheric trace gases, Rev. Geophys., 25, 1441.

Schneider, S. H. (1989) Global Warming, Sierra Club Books, San Francisco.

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