Early one-dimensional box-model estimates of the radiative forcing (e.g., Charlson et al., 1992) using simplified expressions for radiative forcing have been superseded by global calculations using prescribed aerosol concentrations from chemical transport models (CTMs). These studies use either three-dimensional observed fields of for example, clouds, relative humidity and surface reflectance (e.g., Kiehl and Briegleb, 1993; Myhre et al., 1998c), or GCM generated fields (e.g., Boucher and Anderson, 1995; Haywood et al., 1997a) together with the prescribed aerosol distributions from CTMs and detailed radiative transfer codes in calculating the radiative forcing. A growing number of studies perform both the chemical production, transformation, and transportation of aerosols and the radiative forcing calculations (see Chapter 5) with the advantage of correlating predicted aerosol distributions precisely with fields determining aerosol production and deposition such as clouds (e.g., Penner et al., 1998b). Table 6.4 summarises estimates of the radiative forcing from global modelling studies.

Table 6.4: The global and annual mean direct radiative forcing (DRF) for the period from pre-industrial (1750) to present day (2000) due to sulphate aerosols from different global studies. The anthropogenic column burden of sulphate and the source of the sulphate data are also shown together with the normalised radiative forcing. “Frac” indicates a cloud scheme with fractional grid box cloud amount, and “On/off” indicates that a grid box becomes overcast once a certain relative humidity threshold is reached. An asterisk indicates that the maximum hygroscopic growth of the aerosols was restricted to a relative humidity of 90%. The ratio of the Northern to the Southern Hemisphere (NH/SH) DRF and the ratio of the mean radiative forcing over land to the mean radiative forcing over oceans is also shown. NA indicates data is not available. “Langner and Rodhe (1991)s” indicates that the slow oxidation case was used in the calculations.
Study	DRF (Wm-2)	Column burden (mgm-2)	Normalised DRF (Wg-1)	Cloud scheme	DRF NH/SH	DRF land/ocean	Source of sulphate data
Ghan et al. (2001a)	-0.44	4.0	-110	On/off	5.2	1.9	Ghan et al. (2001a)
Jacobson (2001)	-0.32	2.55	-125	Frac	2.7	1.2	Jacobson (2001)
Boucher and Anderson (1995)	-0.29	2.32	-125	Frac	4.3	3.4	Langner and Rodhe (1991)
Graf et al. (1997)	-0.26	1.70	-153	Frac	2.0	NA	Graf et al. (1997)
Feichter et al. (1997)	-0.35	2.23	-157	Frac	4.2	1.4	Feichter et al. (1997)
Kiehl and Briegleb (1993)	-0.28	1.76	-159	Frac	3.3	NA	Langner and Rodhe (1991)s
Iversen et al. (2000)	-0.41	2.40	-167	Frac	4.1	NA	Iversen et al. (2000)
Myhre et al. (1998c)	-0.32	1.90	-169	Frac	6.9	NA	Restad et al. (1998)
van Dorland et al. (1997)	-0.36	2.11	-171	Frac	5.0	NA	van Dorland et al. (1997)
Koch et al. (1999)	-0.68	3.3	-200	Frac	NA	NA	Koch et al. (1999)
Kiehl and Rodhe (1995)	-0.66	3.23	-204	Frac	NA	NA	Pham et al. (1995)
	-0.29	1.76	-165	Frac	NA	NA	Langner and Rodhe (1991)s
Chuang et al. (1997)	-0.43	2.10	-205	On/off*	4.7	2.4	Chuang et al. (1997)
Haywood et al. (1997a)	-0.38	1.76	-215	Frac	4.0	NA	Langner and Rodhe (1991)s
Hansen et al. (1998)	-0.28	1.14	-246	Frac	NA	NA	Chin and Jacob (1996)
Kiehl et al. (2000)	-0.56	2.23	-251	Frac	2.7	1.3	Kiehl et al. (2000)
Haywood and Ramaswamy (1998)	-0.63	1.76	-358	On/off	3.6	2.6	Langner and Rodhe (1991)s
	-0.82	1.76	-460	On/off	5.8	2.7	Kasibhatla et al. (1997)
Penner et al. (1998b) and Grant et al. (1999)	-0.81	1.82	-445	On/off	4.5	2.3	Penner et al. (1998b)

The calculated global mean radiative forcing ranges from -0.26 to -0.82 Wm^-2, although most lie in the range -0.26 to -0.4 Wm^-2. The spatial distribution of the forcings is similar in the studies showing strongest radiative forcings over industrial regions of the Northern Hemisphere although the ratio of the annual mean Northern Hemisphere/Southern Hemisphere radiative forcing varies from 2.0 (Graf et al., 1997) to 6.9 (Myhre et al., 1998c) (see Section 6.14.2 for further details). The ratio of the annual mean radiative forcing over land to that over ocean also varies considerably, ranging from 1.3 (Kiehl et al., 2000) to 3.4 (Boucher and Anderson, 1995). The direct radiative forcing (DRF) is strongest in the Northern Hemisphere summer when the insolation is the highest although different seasonal cycles of the sulphate burden from the chemical transport models result in maximum global mean radiative forcings ranging from May to August (e.g., Haywood and Ramaswamy, 1998), the ratio of the June-July-August/December-January-February radiative forcing being estimated to lie in the range less than 2 (e.g., van Dorland et al., 1997) to > 5 (e.g., Penner et al., 1998b; Grant et al., 1999) with a mean of approximately 3.3. The range of uncertainty in the radiative forcings can be isolated from the uncertainties in the simulated sulphate loadings by considering the range in the normalised radiative forcing i.e., the radiative forcing per unit mass of sulphate aerosol (e.g., Nemesure et al., 1995; Pilinis et al., 1995). Table 6.4 shows that this is substantial, indicating that differences in the radiative forcing are not due solely to different mass loading.

Figure 6.3: The normalised radiative forcing for sulphate aerosol from the intercomparison study of Boucher et al. (1998). A log-normal distribution with a geometric mean diameter of 0.170 µm and a geometric standard deviation of 1.105 together with an aerosol optical depth of 0.20 at 0.55 µm and a Lambertian surface reflectance of 0.15 was assumed. For details of the acronyms and the radiation codes used in the calculations see Boucher et al. (1998).

The optical parameters for sulphate aerosol in each of the global studies vary. Although the single scattering albedo of pure sulphate and sulphate mixed with water is close to unity throughout most of the solar spectrum, some of the studies (e.g., Feichter et al., 1997; van Dorland et al., 1997; Hansen et al., 1998) include some absorption. Charlson et al. (1999) show considerable variation in the specific extinction coefficient used in different studies, particularly when accounting for relative humidity effects. The treatment of the effects of relative humidity and clouds appear to be particularly important in determining the radiative forcing. The studies of Haywood and Ramaswamy (1998), Penner et al. (1998b) and Grant et al. (1999) produce normalised radiative forcings a factor of two to three higher than the other studies. Both Haywood and Ramaswamy (1998) and Penner et al. (1998b) acknowledge that their use of on/off cloud schemes where cloud fills an entire grid box once a threshold relative humidity is exceeded may lead to strong radiative forcings due to strong non-linear relative humidity effects. Chuang et al. (1997) use an on/off cloud scheme and report a radiative forcing lower than these two studies, but the hygroscopic growth is rather suppressed above a relative humidity of 90%. The use of monthly mean relative humidity fields in some of the calculations leads to lower radiative forcings as temporal variations in relative humidity and associated non-linear effects are not accounted for (e.g., Kiehl and Briegleb, 1993; Myhre et al., 1998c). Kiehl et al. (2000) improve the treatment of relative humidity compared to Kiehl and Briegleb (1993) and Kiehl and Rodhe (1995) by improving the relative humidity dependence of the aerosol optical properties and by using interactive GCM relative humidities rather than monthly mean ECMWF analyses, resulting in a larger normalised radiative forcing. Ghan et al. (2001a) perform a sensitivity study and find that application of GCM relative humidities changes the direct radiative forcing by -0.2 Wm^-2 compared to the use of ECMWF analyses because the frequency of occurrence of relative humidities over 90% is higher when using GCM relative humidities. Haywood and Ramaswamy’s (1998) GCM study indicates a stronger radiative forcing when sulphate resides near the surface because the relative humidity and subsequent hygroscopic growth of sulphate particles is higher. GCM sensitivity studies (Boucher and Anderson, 1995) and column calculations (Nemesure et al., 1995) show that the radiative forcing is a strong function of relative humidity but relatively insensitive to chemical composition. Ghan et al. (2001a) suggest a number of reasons for the relatively low DRF from their study, including the relatively large fraction of anthropogenic sulphate in winter when the insolation is lowest, and the fact that sulphate aerosols are smaller in this study and therefore have smaller scattering efficiencies (see also Boucher and Anderson, 1995). The contribution to the global forcing from cloudy regions is predicted to be 4% (Haywood et al., 1997a), 11% (Haywood and Ramaswamy, 1998), 22% (Boucher and Anderson, 1995) and 27% (Myhre et al., 1998c) and hence remains uncertain. However, it should be noted that all of these studies suggest the majority of the global annual mean direct radiative forcing due to sulphate occurs in cloud-free regions. The global mean long-wave radiative forcing has been estimated to be less than 0.01 Wm^-2 and is insignificant (Haywood et al., 1997a).

Boucher and Anderson (1995) investigate the effects of different size distributions, finding a 20 to 30% variation in the radiative forcing for reasonable size distributions. Nemesure et al. (1995) and Boucher et al. (1998) find a much larger sensitivity to the assumed size distribution as sulphate is modelled by much narrower size distributions. Column radiative forcing calculations by fifteen radiative transfer codes of varying complexity (Boucher et al., 1998) show that, for well constrained input data, differences in the computed radiative forcing when clouds are excluded are relatively modest at approximately 20% (see Figure 6.3). This indicates that uncertainties in the input parameters and in the implementation of the radiative transfer codes and the inclusion of clouds lead to the large spread in estimates as suggested by Penner et al. (1994).

Additional column calculations show a weakened radiative forcing when the cloud optical depth is much greater than the aerosol optical depth (Haywood and Shine, 1997; Liao and Seinfeld, 1998) and show that the forcing is insensitive to the relative vertical position of the cloud and aerosol. Haywood et al. (1997b, 1998b) and Ghan and Easter (1998) used a cloud resolving model to investigate effects of sub-grid scale variations in relative humidity and cloud. For their case study, the optical depth and radiative forcing in a GCM sized grid box were underestimated by 60%. Effects of sub-grid scale variations in relative humidity and cloud on a global scale have not been rigorously investigated.

Until differences in estimates of radiative forcing due to sulphate aerosol can be reconciled, a radiative forcing of -0.4 Wm^-2 with a range of -0.2 to -0.8 Wm^-2 is retained. This estimate is based on the range of radiative forcings provided by the model estimates shown in Table 6.4. It is not possible to perform standard statistical procedures because of the limited number of studies and the fact that the resulting DRFs are not normally distributed. However, these results are broadly consistent with the estimates of the uncertainties derived in Chapter 5 (see Sections 5.4.2, and Sections 6.7.8).

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