Indirect Aerosol Forcing, Quasi Forcing, and Climate Response

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Jul 1, 2001 - E-mail: [email protected] mate-model ...... G. P. Ayers, and J. L. Gras, 1994: Coherence between seasonal .... Quart J. Roy. Meteor.
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Indirect Aerosol Forcing, Quasi Forcing, and Climate Response LEON D. ROTSTAYN CSIRO Atmospheric Research, Aspendale, Victoria, Australia

JOYCE E. PENNER Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan (Manuscript received 23 August 2000, in final form 27 November 2000) ABSTRACT The component of the indirect aerosol effect related to changes in precipitation efficiency (the second indirect or Albrecht effect) is presently evaluated in climate models by taking the difference in net irradiance between a present-day and a preindustrial simulation using fixed sea surface temperatures (SSTs). This approach gives a ‘‘quasi forcing,’’ which differs from a pure forcing in that fields other than the initially perturbed quantity have been allowed to vary. It is routinely used because, in contrast to the first indirect (Twomey) effect, there is no straightforward method of calculating a pure forcing for the second indirect effect. This raises the question of whether evaluation of the second indirect effect in this manner is adequate as an indication of the likely effect of this perturbation on the global-mean surface temperature. An atmospheric global climate model (AGCM) is used to compare the evaluation of different radiative perturbations as both pure forcings (when available) and quasi forcings. Direct and indirect sulfate aerosol effects and a doubling of carbon dioxide (CO 2) are considered. For evaluation of the forcings and quasi forcings, the AGCM is run with prescribed SSTs. For evaluation of the equilibrium response to each perturbation, the AGCM is coupled to a mixed layer ocean model. For the global-mean direct and first indirect effects, quasi forcings differ by less than 10% from the corresponding pure forcing. This suggests that any feedbacks contaminating these quasi forcings are small in the global mean. Further, the quasi forcings for the first and second indirect effects are almost identical when based on net irradiance or on cloud-radiative forcing, showing that clear-sky feedbacks are negligible in the global mean. The climate sensitivity parameters obtained for the first and second indirect effects (evaluated as quasi forcings) are almost identical, at 0.78 and 0.79 K m 2 W 21 , respectively. Climate sensitivity parameters based on pure forcings are 0.69, 0.84, and 1.01 K m 2 W 21 for direct sulfate, first indirect, and 2 3 CO 2 forcings, respectively. The differences are related to the efficiency with which each forcing excites the strong surfacealbedo feedback at high latitudes. Closer examination of the calculations of the first indirect effect as a forcing and quasi forcing shows that, although they are in reasonable agreement in the global mean, there are some significant differences in a few regions. Overall, these results suggest that evaluation of the globally averaged second indirect effect as a quasi forcing is satisfactory.

1. Introduction The concept of radiative forcing is useful as a firstorder estimate of the potential climatic importance of various forcing mechanisms. It refers to the change in net radiative flux that results from a change in an atmospheric gas, aerosol, or other radiatively active property, such as land surface type. The Intergovernmental Panel on Climate Change (IPCC; Houghton et al. 1996; Penner et al. 1999) for example, uses the concept to compare the relative climatic importance of a number of different forcings, without the need for complex climate simulations. The concept is based on earlier cliCorresponding author address: Dr. Leon D. Rotstayn, CSIRO Atmospheric Research, PMB1, Aspendale, VIC 3195, Australia. E-mail: [email protected]

q 2001 American Meteorological Society

mate-model calculations, which show that there is an approximately linear relationship between the globalmean radiative forcing at the tropopause and the equilibrium change in global-mean surface temperature (Houghton et al. 1990, 1992). Thus, the change in global-mean surface air temperature at equilibrium can be written as DTs 5 lDF,

(1)

where DF is the global-mean adjusted radiative forcing at the tropopause and l is called the climate sensitivity parameter. The ‘‘adjusted radiative forcing’’ is calculated by allowing the stratospheric temperature to adjust to radiative equilibrium, with the tropospheric and surface temperature held fixed. This definition of radiative forcing is useful because it is a better predictor of DT s for forcings that significantly affect stratospheric tem-

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peratures (Houghton et al. 1994; Forster et al. 1997; Hansen et al. 1997). (The stratosphere adjusts on a timescale of several months, which is much shorter than the decadal timescale required for the surface–troposphere system to adjust to equilibrium.) According to Houghton et al. (1994), the stratospheric adjustment is crucial for changes in stratospheric ozone and is important at the 5%–10% level for changes in some greenhouse gases (such as CO 2 ), but it is less important for changes in aerosols. It is therefore usually ignored in calculations of forcing due to aerosol effects. One useful result of allowing the stratospheric adjustment for forcings that affect the stratosphere is that the net flux at the top of the atmosphere (TOA) is then close to that at the tropopause, because the net radiative flux is constant throughout the stratosphere in radiative equilibrium. The quantification of radiative forcing has historically been accomplished by performing a single climate-model simulation in which the radiative transfer calculation is performed twice—once with the perturbing element changed and once holding it at its preindustrial level. However, this practice has not been possible in evaluating the total forcing associated with the indirect effect of aerosols on clouds. The indirect aerosol effect is composed of two parts: 1) the change in cloud albedo resulting directly from the change in droplet concentration (Twomey 1977) and 2) the change in cloud amount and liquid-water content associated with changes in precipitation efficiency (Albrecht 1989). The climatic importance of the second indirect effect is less well established than that of the first indirect effect, although observational evidence has been provided by Warner (1968) and Rosenfeld (1999, 2000). The first indirect effect may be easily calculated using two radiative transfer calculations within a single climate-model simulation— one with estimates for the present-day droplet concentration and one with estimates for the preindustrial droplet concentration. But the second indirect effect must involve a calculation of not just the change in cloud droplet concentration but also the associated change in precipitation efficiency. The droplet concentration affects the precipitation efficiency of a cloud because, for a given liquid-water content, a larger number of droplets implies that the droplets are smaller. Smaller droplets require more collisions to reach a size that has a significant fall velocity. So an increase in droplet concentration may suppress precipitation, thus increasing cloud liquid-water content and cloud lifetime, which may then result in an increase in the time-averaged cloud amount. The quantification of radiative forcing associated with the second indirect effect thus requires a calculation of the change in cloud liquid-water content and cloud amount. But these changes also affect the temperature and water vapor in a climate model. Thus, the calculation of this forcing has not been accomplished while keeping all other parameters constant. Instead, most researchers (Lohmann and Feichter 1997; Rotstayn 1999, 2000; Lohmann et al. 2000; Ghan et al. 2001; Jones et

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al. 2001) have calculated this forcing as the difference in net irradiance, holding sea surface temperatures (SSTs) fixed but allowing adjustment of the temperature within the atmospheric column (and at the land surface) to the altered cloud amount and liquid-water content. In contrast, Le Treut et al. (1998) chose to regard the second indirect effect as a response, rather than a forcing, and did not estimate a specific forcing associated with changes in precipitation efficiency. The practice of using the difference between two simulations to calculate the forcing due to changes in precipitation efficiency leads to some doubt, regarding whether this forcing can be used to determine the average surface temperature change according to (1). This is because some of the ‘‘forcing’’ may be the result of changes in temperature or water vapor associated with the model’s response to the initial change in precipitation efficiency. We will henceforth refer to a forcing calculated from the difference between two simulations using prescribed present-day SSTs as a quasi forcing. The issue of whether the magnitude of the second indirect effect is adequately evaluated as a quasi forcing is of some importance, since studies with global climate models (GCMs) have found that this effect may be comparable to or larger than the first indirect effect (Lohmann and Feichter 1997; Rotstayn 1999, 2000; Lohmann et al. 2000; Jones et al. 2001). It is important to realize that the use of radiative forcing as a guide to the expected change in surface temperature is only valid to first order, even in the global mean. Hansen et al. (1997) and Forster et al. (2000) have used simplified GCMs to evaluate the extent to which different values of l are obtained for different perturbations, even when each forcing is calculated while keeping all other factors constant. This can occur when different perturbations alter the temperature structure in different ways. Hansen et al. found that the principal mechanism involved changes of lapse rate and decreases (or increases) of large-scale cloud cover in layers that were preferentially heated (or cooled). They also found that if perturbations differed in their variation with latitude, they could result in very different sea-ice albedo feedbacks. They obtained l 5 0.92 for 2 3 CO 2 , l 5 0.72 for a 12% change in solar output, and l 5 1.05 for a 22% change in solar output. Experiments in which surface albedo was increased by 20% over selected continents gave values of l as low as 0.43, and certain idealized experiments involving absorbing aerosols were even less well behaved. Forster et al. (2000) found that perturbations involving CO 2 typically gave a 17% higher sensitivity than perturbations involving solar output and suggested that the radiative forcing concept was valid as a predictor of global-mean surface temperature change to within 30%. Thus, in assessing the evaluation of the second indirect effect as a quasi forcing, it seems reasonable to use the figure of 30% as a benchmark. In this study, we use the Commonwealth Scientific

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and Industrial Research Organisation (CSIRO) GCM as a tool to investigate whether evaluation of the second indirect aerosol effect as a quasi forcing provides a reasonable approximation to a forcing. It is difficult to give a definitive answer to this question, because we are unable to evaluate it as a pure forcing for comparison. However, we can substantially answer it by (a) comparing the climate sensitivity parameters obtained for the first and second indirect effects, and (b) comparing different methods of evaluating both effects to gauge the likely magnitude of feedbacks that contaminate the quasi-forcing calculation. The rationale for using calculations of the first indirect effect to make inferences about the second indirect effect is that they both involve a perturbation to the radiative properties of low clouds, so their horizontal and vertical distributions are expected to be similar. It will also become apparent that their magnitudes are similar in the CSIRO GCM. Thus, we anticipate that their behavior will be similar. For comparison, we will also consider (more briefly) the direct effect of sulfate aerosols and a doubling of CO 2 . Section 2 contains a description of the model and experiments. Section 3 contains results and discussion, and section 4 contains a summary and conclusions. 2. Model and experiments

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cipitation scheme was described in detail by Rotstayn (1997). The scheme incorporates prognostic variables for cloud liquid water and cloud ice, consistent treatments of warm-rain and frozen-precipitation processes, and variable cloud radiative properties. The formation and dissipation of stratiform cloud are calculated using an assumed triangular subgrid distribution (Smith 1990) of the total (vapor plus cloud) water. Cloud water then forms in the part of each grid box in which the totalwater mixing ratio exceeds the saturated value, regardless of the aerosol concentration. However, both the calculation of optical depth and the initiation of precipitation in liquid-water clouds are sensitive to the clouddroplet concentration, which is related to the aerosol concentration as described below. At temperatures between 2408C and 08C, mixed-phase clouds are allowed to exist. The liquid fraction in mixed-phase clouds is calculated following Rotstayn et al. (2000a). The optical depth of liquid-water clouds is

t 5

(2)

where L is the liquid-water path (kg m 22 ), rl is the density of liquid water (kg m 23 ), and r e is the droplet effective radius in meters. The parameterized effective radius is

a. Atmospheric model These experiments use a low-resolution (spectral R21) version of the Mark 3 CSIRO atmospheric GCM. The CSIRO GCM is a spectral model that utilizes the flux form (Gordon 1981) of the primitive equations. Advection of water vapor and cloud water is handled via a semi-Lagrangian scheme, in which the departure points of the flow trajectories are calculated following McGregor (1993), and a quasi-monotone interpolation scheme (Bermejo and Staniforth 1992) is used to prevent the generation of spurious oscillations and ensure nonnegativity of the advected quantities. The R21 model has 18 hybrid vertical levels and a horizontal resolution of approximately 5.68 longitude by 3.28 latitude. The most relevant changes made to the model since the earlier calculation of the indirect aerosol effect by Rotstayn (1999) are the introduction of a new mass-flux convection scheme (Gregory and Rowntree 1990), and some changes to the treatment of stratiform clouds and precipitation, which are described below. In common with other convection schemes used in GCMs, the convection scheme includes only a simple treatment of the microphysics of rainfall generation. Once a critical cloud depth (which differs for land and ocean points) is reached, liquid water in excess of a prescribed threshold falls out of the updraft. There is no dependence of this threshold on the distribution of aerosols. In other words, we consider the second indirect effect only for stratiform clouds. An earlier version of the stratiform cloud and pre-

3L , 2r l re

re 5

1

3Wl 4pr l kNd

2

1/3

,

(3)

where N d is the cloud-droplet concentration (m 23 ), Wl is the liquid-water content in the cloudy part of the grid box (kg m 23 ), and k 5 0.67 in continental air masses or 0.80 in maritime air masses (Martin et al. 1994). Equation (3) gives t the expected N 1/3 d dependence for fixed L. The optical depths are used to calculate the cloud reflectivities and absorptivities required by the model’s shortwave (SW) radiation scheme (Lacis and Hansen 1974), using a delta-Eddington scheme (Slingo 1989). In the earlier calculation of the indirect aerosol effect by Rotstayn (1999), the emissivity of liquid-water clouds was related to t [and hence r e through (3)], but the current version of the model uses a different scheme that relates cloud emissivity directly to L, with no dependence on r e . Thus, calculation of the first indirect effect as a pure forcing does not involve any change in longwave (LW) radiation in the current version of the model. Precipitation of cloud liquid water occurs by autoconversion (collision and coalescence of cloud droplets), collection of cloud liquid water by falling raindrops, and accretion of cloud liquid water by falling ice particles. The dependence of rain formation on clouddroplet concentration enters through the parameterization of autoconversion (Tripoli and Cotton 1980). Autoconversion is suppressed until the mixing ratio of cloud liquid water reaches a critical value

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4 3 qcrit 5 pr l rcrit Nd /r, 3

(4)

where rcrit 5 9.3 mm is a prescribed critical volumemean cloud-droplet radius, N d is the cloud-droplet number concentration (m 23 ), rl is the density of liquid water, and r is the air density. The autoconversion rate varies as N 21/3 , but it is the linear dependence of qcrit on N d d through (4) that effectively controls the response of the model to changes in N d . We use a modification of the autoconversion treatment (Rotstayn 2000), whereby the assumed subgrid distribution of moisture from the condensation scheme is used to calculate the fraction of the cloudy area in a grid box in which the local liquid-water mixing ratio exceeds qcrit . Autoconversion then occurs in this fraction of the cloudy area. Rotstayn (2000) found that this modification increased the magnitude of the calculated second indirect effect from 20.8 to 21.3 W m 22 . Following Boucher and Lohmann (1995), N d is estimated empirically from the mass concentration of sulfate m as Nd 5

5

10 6 3 114.8m 0.48 10 6 3 173.8m 0.26

over oceans, over land,

(5)

with m in micrograms per cubic meter. This means that sulfate is used as a surrogate for all aerosols that act as cloud condensation nuclei (CCN), assuming that the fraction of sulfate in aerosols remains constant. Such a treatment is appropriate for aerosols from industrial regions, since the parameterization is based on measurements in regions impacted by industrial aerosols, but may not apply to aerosols from biomass burning. The sulfate concentration is obtained from monthly mean distributions of sulfate column burden generated by the chemical transport model of Penner et al. (1994) for preindustrial (PI) and present-day (PD) conditions. These distributions are the same as those shown by Rotstayn (1999), who found that the cloud-droplet effective radii generated by the model for the present day agreed quite well with the satellite-retrieved values of Han et al. (1994), although the land–ocean and hemispheric contrasts were weaker in the model than in the observations. The annual-mean, global sulfate burden is 0.20 Tg S (teragrams of sulfur) for the PI case and 0.50 Tg S for the PD case. The sulfate column burdens are distributed in the vertical in such a way that the sulfate mass concentration decreases exponentially with height, using a scale height of 2000 m. A simple treatment of the direct radiative effect of sulfate, which entails a perturbation of the surface albedo (Mitchell et al. 1995), is also included in the model. Our treatment of aerosols and aerosol–cloud interactions is quite simple in some respects. We emphasize that in this study we are using the model as a tool to explore different methods of evaluating radiative perturbations, rather than as a tool to calculate the ‘‘cor-

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rect’’ answer. In particular, we note that, while our result for the total indirect aerosol effect (22.6 W m 22 in the global mean) is not unusually large in comparison with other results obtained using GCMs that include the second indirect effect, it is similar in magnitude to the radiative forcing due to anthropogenic greenhouse gases. Thus, consideration of the observed temperature record would suggest that this result is probably too large. Rotstayn (1999) discusses the simplifications inherent in our calculations of the indirect aerosol effect, and Ghan et al. (2001) includes a detailed discussion of the problems and uncertainties involved in global calculations of the indirect aerosol effect. b. Experiments We have performed a number of model experiments, in which the atmospheric GCM was run either with prescribed SSTs, or coupled to a mixed layer (‘‘q flux’’) ocean model. The prescribed SSTs are interpolated linearly in time each model day from the monthly mean climatological values for the period 1951–80 provided by the Met Office. The mixed layer ocean (MLO) model assumes a mixed layer depth of 50 m in regions away from the sea ice, increasing to 150 m under sea ice. The monthly mean oceanic heat transports used in the MLO runs were calculated using the method of Wilson and Mitchell (1987) from a 10-yr run of the atmospheric GCM forced by the prescribed SSTs. A dynamic treatment of sea ice (O’Farrell 1998) and interactive snow treatment are used in all the experiments, but the albedo of the land surface is prescribed. Thus, surface-albedo feedbacks due to changes in sea ice or snow cover are allowed, but surface-albedo feedbacks due to changes in soil moisture are suppressed. All runs were started on 1 July from an initial state that was generated by another prescribed-SST simulation of the present climate (using a slightly different version of the model). Table 1 summarizes six model runs that were performed using prescribed SSTs, and Table 2 summarizes six otherwise identical runs that used the MLO model to obtain the SSTs. The prescribed-SST runs are used to obtain the quasi forcings, and the MLO runs are used to obtain the equilibrium surface temperature changes. The results from the prescribed-SST runs are based on 20 yr of model output after a 6-month spinup period. The MLO runs are based on 10 yr of model output after equilibration; the equilibration period for each MLO run is given in Table 2. The sulfate distributions used to calculate the direct aerosol effect and to obtain N d in the autoconversion scheme [eq. (4)] and in the radiation scheme [eq. (3)] can be varied independently in the model. So, for example, taking the difference in net irradiance (defined as the net downward radiative flux at the TOA) between the FIXED_PD_CTRL and FIXED_PI_RAD runs gives an estimate of the quasi forcing due to the first indirect effect. Similarly, the difference in net irradiance between the FIXED_PD_CTRL and

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TABLE 1. Details of experiments in which the atmospheric GCM is forced by fixed SSTs. Here PD denotes present-day; PI denotes preindustrial. CO 2 concentration is in parts per million by volume. N d in radiation

N d in autoconversion

Direct sulfate

CO 2 concentration

PD PI PD PI PD PD

PD PD PI PI PD PD

PD PD PD PD PI PD

345 345 345 345 345 690

Experiment FIXED PD CTRL FIXED PI RAD FIXED PI RAIN FIXED PI IND FIXED PI DIR FIXED 2 3 CO2

FIXED_PI_RAIN runs gives an estimate of the quasi forcing due to the second indirect effect, and the difference in net irradiance between the FIXED_PD_CTRL and FIXED_PI_IND runs gives an estimate of the quasi forcing due to the total indirect effect (i.e., the first and second effects operating together). Note that the aerosol quasi forcings are calculated from the FIXED_PD_CTRL run minus the relevant PI run (to give a negative forcing), whereas the 2 3 CO 2 quasi forcing is calculated from the FIXED_2 3 CO2 run minus the FIXED_PD_CTRL run, to give a positive forcing. The MLO runs parallel the prescribed-SST runs. Thus, the difference in surface air temperature between the MLO_PD_CTRL run and each of the other MLO runs gives an estimate of the equilibrium surface air temperature change due to the effect being considered. We will mainly focus on the indirect aerosol effects, but have included the 2 3 CO 2 and direct aerosol calculations for comparison, since these forcings have been studied extensively using GCMs. 3. Results and discussion a. Global-mean forcings Previous studies have shown that the R21 version of the CSIRO GCM provides a generally satisfactory simulation of the present climate by the standards of current GCMs. A detailed evaluation of the model’s simulation of cloudiness and cloud-radiative forcing was presented by Rotstayn (1998) for a slightly earlier version of the model. Quantities especially relevant to the indirect aerosol effect have been evaluated more recently by Rotstayn (1999; effective radius and cloud-droplet con-

centration), and Rotstayn et al. (2000b; precipitation). Some relevant quantities and their global-mean values from the FIXED_PD_CTRL run are cloud cover (64%), liquid-water path over oceans (71 g m 22 ), precipitation rate (2.8 mm day 21 ), SW cloud forcing (244 W m 22 ), and LW cloud forcing (28 W m 22 ). All of these are within the experimental uncertainty of the observational datasets cited by Rotstayn (1998) with the possible exception of the SW cloud forcing, which is a little weaker than the value of 249 W m 22 from the Earth Radiation Budget Experiment. Table 3 shows a number of globally averaged quantities from the prescribed-SST runs, chosen to give an indication of the extent to which clear-sky or cloud feedbacks may be occurring in these runs. Note that, whereas the SSTs are fixed in these runs, the land surface temperature can vary. The first column of Table 3 shows that small changes in land surface temperature did indeed occur in these runs. The small changes in precipitable water (column water vapor) are in the same sense as the land surface temperature changes, as one would expect. The magnitude of the changes in these quantities would suggest that clear-sky feedbacks are probably small in the aerosol runs, and that they are similar in the FIXED_PI_RAD and FIXED_PI_RAIN runs. The larger warming of the land surface in the FIXED_2 3 CO2 run would suggest that the resulting negative LW feedback in this run might be substantial (since LW emission varies with temperature to the fourth power). Note that, even though the global-mean quasi forcing for the total indirect aerosol effect is a substantial fraction of the quasi forcing for 2 3 CO 2 (see Table 4), the change in land surface temperature is much smaller in

TABLE 2. Details of experiments in which the atmospheric GCM is coupled to a mixed layer ocean model. Here PD denotes present-day; PI denotes preindustrial. The CO 2 concentration: ppmv, equilibration period: years.

Experiment MLO PD CTRL MLO PI RAD MLO PI RAIN MLO PI IND MLO PI DIR MLO 2 3 CO2

N d in radiation

N d in autoconversion

Direct sulfate

CO 2 concentration

Equilibration period

PD PI PD PI PD PD

PD PD PI PI PD PD

PD PD PD PD PI PD

345 345 345 345 345 690

26.5 26.5 26.5 41.5 26.5 46.5

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ROTSTAYN AND PENNER TABLE 3. Globally averaged quantities from the prescribed-SST runs.

Experiment FIXED PD CTRL FIXED PI RAD FIXED PI RAIN FIXED PI IND FIXED PI DIR FIXED 2 3 CO2

Land surface temperature (K)

Precipitable water (mm)

Low cloud (%)

Liquid-water path (g m22 )

High cloud (%)

281.23 281.26 281.24 281.35 281.39 281.70

21.98 22.02 21.99 22.06 22.05 22.15

42.30 42.29 41.39 41.31 42.37 42.11

63.39 63.32 57.95 57.88 63.68 62.71

31.60 31.68 31.65 31.57 31.67 31.28

the FIXED_PI_IND run than in the FIXED_2 3 CO2 run, because the indirect effect in the model acts more strongly over the ocean (2.9 W m 22 ) than over the land (2.1 W m 22 ). This is due to the lower albedo of the ocean surface, and the fact that the parameterization (5) causes clouds over oceans to be more susceptible to increases in CCN (for which sulfate mass is a surrogate). The ‘‘flatter’’ form of (5) over land than over ocean is broadly consistent with the idea that continental clouds are less susceptible to the effects of anthropogenic increases in CCN, because there are more natural CCN over land than over ocean. By far the largest changes in low cloud and liquidwater path occur in the two runs (FIXED_PI_RAIN and FIXED_PI_IND) in which autoconversion is directly perturbed. The changes in low cloud and liquid-water path due to the direct aerosol and first indirect effects are much smaller. This is encouraging, as it suggests that the ‘‘signal’’ due to the second indirect effect is much larger than the effect of feedbacks. The FIXED_2 3 CO2 run has the largest change in high cloud cover. This is consistent with the idea that the aerosol radiative perturbations occur near the surface, whereas the 2 3 CO 2 perturbation also acts aloft. The decreases in both high and low cloud cover in the FIXED_2 3 CO2 run suggest that the quasi forcing for 2 3 CO 2 might be contaminated by positive SW and negative LW cloud feedbacks.

Table 4 shows the calculated quasi forcings associated with the different aerosol perturbations and with a doubling of CO 2 . The uncertainty in the global-mean quasi forcings due to the interannual variability of the simulations is relatively small in comparison with the magnitude of the quasi forcings. For example, a 95% confidence interval for the quasi forcing due to the first indirect effect (taking the 20 annual-mean differences as the data points) is 21.41 6 0.08 W m 22 if it is based on the change in net cloud-radiative forcing. Halfwidths of 95% confidence intervals for the other quasiforcing components generally lie in the range 0.04–0.10. Thus, some of the LW and clear-sky components of the quasi forcings are comparable to or smaller than the uncertainty due to the interannual variability of these quantities; those that do not differ from zero with a 5% level of significance are enclosed in parentheses. For the first indirect and direct aerosol effects and for 2 3 CO 2 , we have also calculated pure forcings in which everything else is held fixed, marked with an asterisk in Table 4. For the first indirect and direct aerosol effects, this was done using an extra call to the SW radiation scheme at each radiation time step during the FIXED_PD_CTRL run. For the first indirect effect, the extra call used preindustrial droplet concentrations in the calculation of the cloud optical depth. For the direct aerosol effect, the extra call used a smaller surfacealbedo perturbation, based on the preindustrial sulfate

TABLE 4. Calculated global-mean quasi forcings, equilibrium annual-mean surface air-temperature changes, and climate-sensitivity parameters for different aerosol perturbations and for a doubling of CO 2 . Where available, pure forcings and the corresponding climate-sensitivity parameters are marked with an asterisk. Also shown is the breakdown of each total forcing into its shortwave versus longwave and cloud-forcing (CF) versus clear-sky (CS) components. Quasi forcing components that do not differ from zero with a 5% level of significance are enclosed in parentheses. Radiative forcing (W m22 ) Shortwave

First indirect Second indirect Total indirect Direct sulfate 2 3 CO 2

Longwave

Total

CF

CS

CF

CS

21.46 21.35* 21.32 22.57 20.75 20.80* 3.29 3.48*

21.44 21.35* 21.39 22.70 0.54 0.52* 0.46 0.08*

20.07 0 20.05 20.11 21.42 21.32* 0.33 0.08*

(0.03) 0 0.09 0.13 0.00 0 20.84 20.53*

(0.02) 0 (0.02) 0.11 0.13 0 3.34 3.85*

DT s (K)

l (K m 2 W 21 )

21.14

0.78 0.84* 0.79 0.87 0.73 0.69* 1.07 1.01*

21.04 22.24 20.55 3.52

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distribution. We follow the usual practice of ignoring the stratospheric adjustment for the aerosol forcings, as was explained in the introduction. The interannual variability in the calculation of the pure forcings is much smaller than that given above for the quasi forcings; a 95% confidence interval for the first indirect effect is 21.352 6 0.005 W m 22 . The 2 3 CO 2 forcing is from an offline radiative calculation (Zhang et al. 1994). To perform this calculation, the entire atmospheric state of the FIXED_PD_CTRL run was saved every 18 h during one year, and the model’s radiation scheme was then applied to each of these states in turn. The offline calculation was then repeated with the atmospheric CO2 concentration doubled. After allowing the stratosphere to adjust to the modified radiative fluxes as referred to in the introduction, the TOA fluxes from the doubledCO 2 run were compared with those from the first offline calculation to provide the forcings for 2 3 CO 2 given in Table 4. For perturbations for which a pure forcing is available, the difference between the quasi forcing and the pure forcing gives the feedback that is contaminating the quasi forcing. Thus, for example, the total feedback that is contaminating the estimate of the first indirect effect as a quasi forcing is 20.11 W m 22 in the global mean. This feedback can be broken down into its SW versus LW and cloud-forcing versus clear-sky components, by taking the difference between the appropriate pure-forcing and quasi-forcing components. [We use the Method II cloud forcing of Cess and Potter (1988), in which the clear-sky fluxes are calculated by repeating the radiation call with all clouds removed, and the cloud forcing is defined as the difference between the all-sky flux and the clear-sky flux.] For the first indirect effect, the clear-sky and LW components are all identically zero, so the LW and clear-sky feedbacks can be read directly from the second line of Table 4. As was noted in the introduction, we are unable to calculate a pure forcing for the second indirect effect, so we are unable to calculate the total feedback that applies. However, we may assume that for a ‘‘pure’’ forcing for the second indirect effect, the clear-sky components would be zero, so we can read the clear-sky feedbacks directly from the third line of Table 4. Note that for perturbations that do not directly affect the clear-sky flux, an alternative method of obtaining the clear-sky feedback is to take the difference between the quasi forcings calculated from the change in total TOA irradiance and from the change in total cloud– radiative forcing. This method works for both indirect effects, but is not valid for perturbations that directly affect the clear-sky flux. For the direct aerosol effect, the differences between the pure and quasi forcings show that the feedback components are again of the order of 0.1 W m 22 or smaller. Note that there is a substantial change in the SW cloud forcing, even when the direct aerosol effect is calculated as a pure forcing, because changing the surface albedo

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changes the radiative forcing of clouds over that surface. Thus, for the aerosol effects, the quasi forcings seem to be a reasonably good approximation to the pure forcings, at least in the global mean. However, evaluation of the effect of a doubling of CO 2 as a quasi forcing appears to be a poor approximation, because it is affected by substantial positive SW and negative LW cloud feedbacks, as was suggested above. It is also affected by a substantial negative LW clear-sky feedback. Note that even the pure 2 3 CO 2 forcing includes cloud-forcing components as well as the larger clear-sky components. This is because there is overlap between the absorption by CO 2 and clouds, so the all-sky and clear-sky radiative fluxes respond differently to the doubling of CO 2 . Because of the cancellation between the SW and LW feedback components, the net quasi forcing differs by only 0.19 W m 22 from the pure forcing. The latter is a little smaller than the value of 3.7 W m 22 calculated by Myhre et al. (1998). b. A closer look at the indirect-effect forcings Consideration of global means, as in the previous section, does not rule out the possibility that there are compensating geographical changes. It is therefore important to consider the geographical distribution of the first and second indirect effects. Figure 1 shows the annually averaged first indirect effect calculated as a forcing, as a quasi forcing, and as a quasi forcing based on the change in total cloud-radiative forcing (instead of net irradiance). The first point is that the quasi forcings shown in Figs. 1a and 1b are much noisier than the pure forcing shown in Fig. 1c. Recall from the previous section that for the indirect aerosol effects, the clear-sky feedback can be calculated from the difference between the quasi forcing based on net irradiance and the quasi forcing based on cloudradiative forcing. The differences between Figs. 1a and 1b are generally small, showing that the clear-sky feedbacks are generally small. Also, the main features of the smoother distribution in Fig. 1c are similar to those in Figs. 1a and 1b. However, regionally, there are some obvious differences between Figs. 1b and 1c, possibly indicating the presence of substantial cloud feedbacks in these areas. To check whether the features of the quasi-forcing distribution shown in Fig. 1a are statistically significant, we have computed t scores corresponding to this distribution, taking the 20 annual means from the FIXED_PD_CTRL and FIXED_PI_RAD simulations at each grid point as the individual data points. These are plotted in Fig. 2a, with light shading indicating differences significant at the 10% level and dark shading indicating differences significant at the 1% level, based on 38 (2 3 20 2 2) degrees of freedom. The t scores show that the major features of the quasi-forcing distribution are highly significant. The t scores for the dif-

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FIG. 1. Annual mean first indirect (Twomey) effect calculated (a) as a quasi forcing based on net TOA radiation, (b) as a quasi forcing based on net cloud-radiative forcing, and (c) as a pure forcing (using an extra call to the shortwave radiation scheme at each radiation time step during the FIXED_PD_CTRL run). Contours are 213, 211, 29, 27, 25, 23, 21, 1, and 3 W m 22 . Shading scales with intensity: Ls and Hs depict max and min values within contour.

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FIG. 2. Distribution of t scores for (a) the calculation of the first indirect effect as a quasi forcing based on net TOA radiation, (b) for the clear-sky feedbacks contaminating the calculation of the first indirect effect as a quasi forcing, (c) for the cloud feedbacks contaminating the calculation of the first indirect effect as a quasi forcing. The light shading shows results significant at the 10% level ( | t | . 1.69) and the dark shading shows results significant at the 1% level ( | t | . 2.71).

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FIG. 4. The t scores for annual mean–zonal mean total feedbacks over land and ocean that contaminate the calculation of the first indirect effect as a quasi forcing. The t scores with magnitude greater than 2.0 are significant at the 5% level.

FIG. 3. Annual mean–zonal mean feedbacks over (a) land and (b) ocean that contaminate the calculation of the first indirect effect as a quasi forcing.

ferences between Figs. 1a and 1b (i.e., the clear-sky feedbacks) are shown in Fig. 2b. These are generally not statistically significant, with the exception of some relatively large clear-sky feedbacks at high latitudes. These are due to local changes in sea-ice cover, and could have been suppressed by using prescribed sea-ice distributions in the simulations. The t scores for the differences between Figs. 1b and 1c (i.e., the cloud feedbacks) are shown in Fig. 2c. The cloud feedbacks are only statistically significant over a few regions. To see the feedbacks more clearly, it is useful to look at zonal averages of the total, clear-sky, and cloud feedbacks over land and ocean separately (Fig. 3). Clearsky feedbacks are generally smaller than 0.5 W m 22 in the zonal mean, except for some regions at high latitudes, where relatively large feedbacks occur due to seaice changes. Feedbacks are generally smaller over ocean than over land, despite the fact that overall the forcing is larger over ocean (21.62 W m 22 ) than over land (21.08 W m 22 ). This result is expected, because the SSTs were held fixed, whereas the land surface temperature was allowed to vary in the simulations. Ghan

et al. (1990) observed little feedback in their simulations of the indirect effect, but their forcing was over the ocean only. Excluding the sea-ice feedback discussed above, the most substantial feature of our results is the relatively large negative feedback over tropical land. The total feedbacks zonally averaged t scores over land and ocean are shown in Fig. 4, and indicate that in the zonal mean, the feedbacks are only significantly different from zero over narrow regions. Figure 5 shows the annually averaged second indirect effect calculated as a quasi forcing. Figure 5a is based on the net irradiance, and Fig. 5b is based on the net cloud-radiative forcing. The first point about Fig. 5 is that the distribution of the forcing is similar to that for the first indirect effect. Also, the main features of two distributions are similar, suggesting that the clear-sky feedbacks are generally small. The t scores for the quasiforcing distribution from Fig. 5a (not shown), confirm that the main features of the quasi-forcing distribution are again highly significant. The t scores for the differences between Figs. 5a and 5b (i.e., the clear-sky feedbacks, not shown) confirm that the feedbacks are mostly not statistically significant. To show the clearsky feedbacks more clearly, the zonally averaged differences between Figs. 5a and 5b over land and ocean are plotted in Fig. 6. The clear-sky feedbacks are similar in magnitude to those shown for the first indirect effect in Fig. 3b. They are mostly less than 0.5 W m 22 in the zonal mean, except for some small areas at high latitudes, where changes in sea ice can result in larger (negative) clear-sky feedbacks. How do these feedbacks compare in magnitude with the forcings themselves? Figure 7 shows the zonally and annually averaged first and second indirect effects over land and ocean, both calculated as quasi forcings, based on the net irradiance as in Figs. 1a and 5a. It is seen that the largest quasi forcings occur over the Northern Hemisphere (NH) oceans, and that the second indirect

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FIG. 5. Annual mean second indirect (Albrecht) effect calculated (a) as a quasi forcing based on net TOA radiation, and (b) as a quasi forcing based on net cloud radiative forcing. Contours are 213, 211, 29, 27, 25, 23, 21, 1, and 3 W m 22 . Shading scales with intensity: Ls and Hs depict max and min values within contour.

FIG. 6. Annual mean–zonal mean clear-sky feedbacks over land and ocean that contaminate the calculation of the second indirect effect as a quasi forcing.

FIG. 7. Annual mean–zonal mean first and second indirect effects over land and ocean, calculated as quasi forcings.

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FIG. 8. Variation with time of the global mean, annual mean surface air temperature from six runs in which the atmospheric GCM was coupled to a mixed layer ocean model.

FIG. 9. Annual mean–zonal mean radiative forcing due to a doubling of CO 2 , the first indirect aerosol effect, and the direct aerosol effect.

effect gives larger (more negative) values there than the first indirect effect. In the Southern Hemisphere (SH), both effects give quasi forcings of around 1 W m 22 or less in the zonal mean, so the feedbacks shown previously are a substantial fraction of the quasi forcings in the zonal mean. However, where the indirect effect is strongest (over oceans in the NH), the feedbacks are clearly smaller in magnitude than the quasi forcings.

structure of the perturbation is similar for the two indirect effects. It confirms that any errors introduced by the evaluation of the second indirect effect as a quasi forcing are relatively small in our model in the global mean. The climate sensitivity parameter for the total indirect effect is a little larger than those for the first and second indirect effects, suggesting that these two effects may interact with each other in a nonlinear manner, or that some of the feedbacks in the MLO runs operate in a nonlinear manner (e.g., Colman et al. 1997). The climate sensitivity parameter is somewhat larger for the 2 3 CO 2 case (l 5 1.01) than for the aerosol cases. If we compare the three values of l obtained from the pure forcings, we see that 2 3 CO 2 has a larger climate sensitivity than the first indirect effect, which in turn has a larger climate sensitivity than the direct aerosol effect. These differences can be understood in terms of the variation with latitude of the different forcings (Fig. 9), which determines their ability to excite the strong surface-albedo feedback at high latitudes. The 2 3 CO 2 forcing is relatively uniform with latitude, whereas the aerosol forcings drop off sharply away from the NH midlatitudes. The ratio (forcing poleward of 608)/(global-mean forcing) is 0.76 for 2 3 CO 2 , 0.42 for the first indirect effect, and 0.37 for the direct aerosol effect. Thus, the 2 3 CO 2 forcing is the most efficient at exciting the surface-albedo feedback at high latitudes, and the direct aerosol forcing is the least efficient. A further reason that l for the direct effect is smaller than for the indirect effect is that the direct effect is weaker over oceans than over land, whereas the indirect effect is stronger over oceans than over land. Therefore, the direct effect is less efficient at exciting the strong seaice albedo feedback. (The sea-ice albedo feedback is stronger overall than the snow cover albedo feedback over land. This is confirmed by offline calculations from the MLO_2 3 CO2 run, where forcing is similar over land and ocean.) Recall from the introduction that Hansen et al. (1997) also obtained a relatively small value

c. Response of the model As was noted in the introduction, an important reason for using the concept of radiative forcing is that it is considered to provide a first-order estimate of the importance of a climatic perturbation, and in particular of its effect on global-mean surface air temperature. This is only valid if the climate sensitivity parameters determined for different perturbations are similar. Though there are potentially important responses of precipitation and precipitation patterns to the indirect effect (Rotstayn et al. 2000b), for simplicity we focus here on the temperature response. Figure 8 shows the time variation of the globally and annually averaged surface air temperature from the MLO runs. In each run, time-averaged quantities shown in this section are based on the last 10 years of integration, during which period the model is in approximate equilibrium. Table 4 shows that the climate sensitivity parameters for the different aerosol perturbations all lie in the range 0.69–0.87. In other words, the variation is within the 30% range suggested by Forster et al. (2000), whether they are evaluated as forcings or quasi forcings. The variation is smaller than this for the indirect aerosol effects, and the climate sensitivity parameters for the first and second indirect effects (evaluated as quasi forcings) are almost identical, at 0.78 and 0.79 K m 2 W 21 , respectively. This relatively small variation in l is presumably due to the fact that the horizontal and vertical

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response due to the (total) indirect effect, with the latter shown as a warming (PI minus PD) for comparison. In the NH, the zonally averaged responses are similar, but as expected the response to the indirect effect is much weaker in the SH. d. Other possible feedbacks

FIG. 10. Annual mean–zonal mean change in surface air temperature at equilibrium due to (a) the first and second indirect effects over land and ocean, (b) a doubling of CO 2 and the total indirect effect (the latter shown as a warming).

of l for perturbations of surface albedo over NH land, that is, for perturbations similar to the direct aerosol effect as included in our model. We anticipated a similar response to the first and second indirect effects, because of their similar magnitudes and distributions. Figure 10a shows the change in annual mean surface air temperature at equilibrium due to the first and second indirect effects, zonally averaged over land and ocean. Overall, Fig. 10 confirms the anticipated result. Both effects show a larger response in the NH where the forcing is larger, and both show their largest response over high-latitude oceans in the NH, due to a strong sea-ice albedo feedback. Differences in the response are broadly consistent with differences in the quasi forcings shown in Fig. 7. For example, over midlatitude oceans in the NH, the response to the second effect is a little stronger than that to the first effect, and this is consistent with the quasi forcing for the second effect being stronger there. Conversely, the response to the second effect is generally weaker in the Tropics, where its quasi forcing is also weaker. Figure 10b compares the response due to a doubling of CO 2 with the

A limitation of the above experiments is that the GCM did not include an interactive sulfur cycle. Instead, the sulfate distributions were calculated offline. In interactive models, aqueous oxidation of sulfur dioxide (SO 2 ) in cloud droplets is an important source of sulfate, and scavenging by precipitation is an important sink of sulfate. This means that we have ignored some possible feedbacks, such as the suppression of precipitation scavenging of sulfate and SO 2 due to the second indirect effect. Note that, for the purpose of the present paper, this feedback is only important if the scavenging would differ substantially between the prescribed-SST and the MLO experiments (in which SST is allowed to change). Other aspects of the sulfur cycle, such as reaction rates, or the amount of SO 2 that dissolves in cloud water, may also be affected by changes in temperature. To ascertain whether this omission is important, we have repeated our calculations for the total indirect aerosol effect using a later version of the CSIRO GCM, which includes an interactive sulfur cycle. Prognostic variables are SO 2 and dimethyl sulfide (DMS) as gases, and sulfate as an aerosol. Transport of these species by advection and vertical turbulent mixing follows the treatment of cloud water in the GCM (Rotstayn 1997). The sulfur chemistry and the treatment of wet and dry deposition follows Feichter et al. (1996). Emissions for the PD and PI scenarios are as described by Lohmann et al. (2000). Another important difference in the later version of the GCM is that the subgrid autoconversion treatment is not used in this version. Instead, we have returned to the standard treatment described by Rotstayn (2000), in which autoconversion occurs in the entire cloudy part of each grid box when the autoconversion threshold is exceeded, and rcrit 5 7.5 mm in (4). Since the subgrid autoconversion treatment was found to increase the magnitude of the modeled second indirect effect by 62%, returning to the standard treatment is expected to substantially reduce its magnitude. In other important respects, the model remains as described above. Repeating the FIXED_PD_CTRL and FIXED_PI_IND experiments with this version of the model gave a net quasi forcing of 21.56 W m 22 for the total indirect effect. The annual-mean sulfate burdens were 0.23 Tg S in the PI run and 0.68 Tg S in the PD run, both somewhat higher than the burdens used above. The reduced quasi forcing (compared with 22.57 W m 22 obtained previously) is substantially due to the change of autoconversion treatment. Another factor is likely to be the inclusion of an interactive sulfur cycle, since both

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Feichter et al. (1997) and Jones et al. (2001) found that significant increases in indirect forcing resulted from the use of time-averaged sulfate fields. Repeating the MLO_PD_CTRL and MLO_PI_IND runs with the interactive sulfur cycle gave an equilibrium global-mean surface air temperature change of 21.26 K. Thus, l 5 0.81, similar to the values obtained above. The annual-mean sulfate burdens were 0.22 Tg S in the PI run, and 0.68 Tg S in the PD run. These are close to the values obtained in the prescribed-SST runs, suggesting that temperature-related feedbacks on the sulfur cycle are not important in the model in the global mean. Note that possible feedbacks due to the increased production of DMS by oceanic phytoplankton in a warmer climate (Charlson et al. 1987; Boers et al. 1994) are not included in the model, since the distribution of DMS in seawater is prescribed. Other possible feedbacks involve processes that may not be resolved by our model. The indirect effect works mainly on boundary layer clouds, which are not well simulated by GCMs, because of their coarse vertical resolution and simplified treatments of boundary layer turbulence and aerosol–cloud interactions. An example of a process that may not be resolved in a GCM is the absorption feedback on the first indirect effect discussed by Boers and Mitchell (1994). They found that the thermodynamic tendency of the cloud to stabilize itself against changes in the absorption of solar radiation caused the cloud optical depth to vary with droplet concentration differently than the expected t ; N 1/3 d . It is important to perform further studies of the indirect aerosol effect using cloud-resolving models, in addition to GCMs. 4. Summary and conclusions We have used an atmospheric GCM (AGCM) combined with monthly mean sulfate distributions calculated by a chemical transport model, to investigate whether evaluation of the second indirect aerosol effect as a quasi forcing provides a reasonable approximation to a forcing. We defined a quasi forcing as the difference in net irradiance between two simulations that use prescribed SSTs. The question cannot be answered directly, because there is no straightforward method of calculating the second indirect effect as a (pure) forcing. So, we used calculations of the first indirect effect as both a forcing and quasi forcing to help us draw conclusions about the second indirect effect. We justified this by showing that the magnitude and spatial distribution of the two effects, as well as the surface temperature response of our model, were similar. Our main criteria were (a) whether the climate sensitivity parameter (l) obtained by evaluating the second indirect effect as a quasi forcing was similar to that obtained for other similar perturbations (in particular the first indirect effect), and (b) whether the quasi-forcing calculation was contaminated by large feedbacks.

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Criterion (a) is relevant to whether the quasi forcing is adequate as a first-order predictor of the change in global-mean surface air temperature using (1). To answer (b), we had to turn to calculations of the first indirect effect for guidance regarding the likely magnitude of cloud feedbacks. The climate sensitivity parameters obtained for the first and second indirect effects (evaluated as quasi forcings) were almost identical, at 0.78 and 0.79 K m 2 W 21 , respectively. Thus, criterion (a) is satisfied, at least in our model. For the global-mean direct and first indirect effects, evaluation as a quasi forcing gave results that differed by less than 10% from the pure forcing. This suggests that any feedbacks contaminating these quasi forcings are not substantial in the global mean. Further, the quasi forcings for the first and second indirect effects were almost identical when based on net irradiance or on cloud-radiative forcing, showing that clear-sky feedbacks are negligible in the global mean. Climate sensitivity parameters based on pure forcings were 0.69, 0.84, and 1.01 K m 2 W 21 for direct sulfate, first indirect, and 2 3 CO 2 forcings, respectively. The differences are related to the efficiency with which each forcing excites the strong surface–albedo feedback at high latitudes. This provides further evidence that changing the nature of the perturbation can result in larger changes in l than changing the method of evaluating the forcing. Closer examination of the calculations of the first indirect effect as a forcing and quasi forcing showed that although they are in reasonable agreement in the global mean, there are some significant feedbacks that affect the quasi-forcing calculation in a few regions. Clear-sky feedbacks were generally smaller than cloud feedbacks. Some locally large clear-sky feedbacks could have been eliminated by running the model with fixed sea ice distributions. In most regions the clear-sky and cloud feedbacks were not significantly different from zero. It was similarly found for the second indirect effect (for which we were unable to evaluate the cloud feedbacks) that the clear-sky feedbacks affecting the quasi forcing were generally small. Any errors associated with ignoring these feedbacks should be considered in relation to the use of (1) to estimate the change in surface air temperature. This equation is only expected to be valid to within roughly 30% in the global mean (for fixed l), and it is well known that this equation does not hold on a regional basis. Recalculation of the quasi forcing and response for the total indirect aerosol effect, using a later version of the AGCM that includes an interactive sulfur cycle, gave l 5 0.81. This is similar to the values obtained using offline sulfate distributions. Further, temperature feedbacks on the sulfur cycle were not substantial in the global mean, suggesting that omission of an interactive sulfur cycle in the above experiments has not significantly affected our conclusions. Overall, our results suggest that evaluation of the

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globally averaged second indirect effect as a quasi forcing is satisfactory. As always, one should be cautious about generalizing the results from a single GCM to other models, so we suggest that it would be useful to perform similar studies using other GCMs. Acknowledgments. The authors thank Martin Dix for his assistance with the 2 3 CO 2 forcing calculation; and Brian Ryan, Martin Dix, and the anonymous reviewers for their perceptive comments on versions of this paper. Thanks are also due to Ulrike Lohmann for her help in putting together the version of the model with the interactive sulfur cycle. This work is partly funded through Australia’s National Greenhouse Research Program. J.E.P. acknowledges support from the Department of Energy Atmospheric Radiation Measurement (ARM) Program. REFERENCES Albrecht, B. A., 1989: Aerosols, cloud microphysics, and fractional cloudiness. Science, 245, 1227–1230. Bermejo, R., and A. Staniforth, 1992: The conversion of semi-Lagrangian advection schemes to quasi monotone schemes. Mon. Wea. Rev., 120, 2622–2632. Boers, R., and R. M. Mitchell, 1994: Absorption feedback in stratocumulus clouds: Influence on cloud top albedo. Tellus, 46A, 229–241. ——, G. P. Ayers, and J. L. Gras, 1994: Coherence between seasonal variation in satellite-derived cloud optical depth and boundary layer CCN concentrations at a mid-latitude Southern Hemisphere station. Tellus, 46B, 123–131. Boucher, O., and U. Lohmann, 1995: The sulfate-CCN-cloud albedo effect. A sensitivity study with two general circulation models. Tellus, 47B, 281–300. Cess, R. D., and G. L. Potter, 1988: A methodology for understanding and intercomparing atmospheric climate feedback processes in general circulation models. J. Geophys. Res., 93, 8305–8314. Charlson, R. J., J. E. Lovelock, M. O. Andreae, and S. G. Warren, 1987: Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate. Nature, 326, 655–661. Colman, R. A., S. B. Power, and B. J. Mcavaney, 1997: Non-linear climate feedback analysis in an atmospheric general circulation model. Climate Dyn., 13, 717–731. Feichter, J., E. Kjellstro¨m, H. Rodhe, F. Dentener, J. Lelieveld, and G.-J. Roelofs, 1996: Simulation of the tropospheric sulfur cycle in a global climate model. Atmos. Environ., 30, 1693–1707. ——, U. Lohmann, and I. Schult, 1997: The atmospheric sulfur cycle in ECHAM-4 and its impact on the shortwave radiation. Climate Dyn., 13, 235–246. Forster, P. M. D. F., R. S. Freckleton, and K. P. Shine, 1997: On aspects of the concept of radiative forcing. Climate Dyn., 13, 547–560. ——, M. Blackburn, and R. G. K. P. Shine, 2000: An examination of climate sensitivity for idealised climate change experiments in an intermediate general circulation model. Climate Dyn., 16, 833–849. Ghan, S. J., K. E. Taylor, and J. E. Penner, 1990: Model test of CCNcloud albedo climate forcing. Geophys. Res. Lett., 17, 607–610. ——, R. Easter, E. C. H. Abdul-Razzak, Y. Zhang, L. Leung, N. Laulainen, R. Saylor, and R. Zaveri, 2001: A physically-based estimate of radiative forcing by anthropogenic sulfate aerosol. J. Geophys. Res., 106, 5279–5293. Gordon, H. B., 1981: A flux formulation of the spectral atmospheric equations suitable for use in long term climate modeling. Mon. Wea. Rev., 109, 56–64.

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