Since the SAR there have been a number of more refined three-dimensional global model estimates of the radiative forcing due to black carbon (BC) aerosol from fossil fuel burning which have superseded calculations using a simple expression for the radiative forcing where the contribution from cloudy regions was not included (e.g., Chylek and Wong, 1995; Haywood and Shine, 1995). These estimates now include the contribution to the total radiative forcing from areas where BC exists either above or within clouds, although the treatment of BC within clouds remains crude. Table 6.5 includes recent global annual mean estimates of the radiative forcing due to BC aerosol from fossil fuels. Haywood et al. (1997a) and Myhre et al. (1998c) assumed that fossil fuel BC was directly proportional to the mass of sulphate from Langner and Rodhe (1991) and Restad et al. (1998), respectively, by applying a 7.5% mass scaling (equivalent to a global mean burden of approximately 0.13 mgm^-2 to 0.14 mgm^-2). Global annual mean radiative forcings of +0.20 Wm^-2 and +0.16 Wm^-2 are calculated for external mixtures. Both studies suggest that BC internally mixed with sulphate will exert a stronger forcing although the method of mixing was fairly crude in both of these studies. These estimates of the radiative forcing were performed before global modelling studies for BC were generally available.

Table 6.5: The global and annual mean direct radiative forcing for the period from pre-industrial (1750) to present day (2000) due to black carbon (BC) and organic carbon (OC) aerosols from different global studies. The anthropogenic column burden of BC and OC is shown, where appropriate, together with the normalised direct radiative forcing (DRF).
Aerosol	Author and type of study	Mixing or optical parameters	DRF (Wm-2)	Column burden (mgm-2)	Normalised DRF (Wg-1)	Remarks
Fossil fuel BC	Haywood et al. (1997a)	External	+0.20	0.13	1525	GCM study. 7.5% mass scaling of BC to SO4 assumed. SO4 from Langner and Rodhe (1991) (slow oxidation case).
		Internal with sulphate	+0.36		2770	Internal mixing approximated by volume weighting the refractive indices of BC and SO4.
	Myhre et al. (1998c)	External	+0.16	0.14	1123	Three-dimensional study using global climatologies for cloud, surface reflectance etc. 7.5% mass scaling of BC to SO4 assumed. SO4 from Restad et al. (1998).
		Internal with sulphate	+0.42		3000	Internal mixing approximated by volume weighting the refractive indices of BC and SO4
	Penner et al. (1998b) and Grant et al. (1999)	Internal with fossil fuel OC	+0.20	0.16	1287	BC modelled using chemical transport model and GCM.
	Cooke et al. (1999)	External	+0.17	0.14	1210	BC modelled using chemical transport model and GCM.
	Haywood and Ramaswamy (1998)	External mixture	+0.2	0.13	1500	Three-dimensional GCM study using Cooke and Wilson (1996) BC data scaled to Liousse et al. (1996) total BC mass. 50% of the BC mass assumed to be from fossil fuels.
Fossil fuel OC	Penner et al. (1998b)	Internal/external with fossil fuel BC	-0.04 to -0.24	-0.7	-60 to -340	OC modelled using chemical transport model and GCM. Weakest estimate corresponds to internal mixing with BC, strongest estimate corresponds to external mixing with BC.
	Cooke et al. (1999)	External mixture	-0.02	0.34	-70	OC modelled using chemical transport model and GCM. May be more negative due to effects of RH and assumption of partial absorption of OC.
	Myhre et al. (2001)	External mixture	-0.09	0.66	-135	Three-dimensional study using global climatologies for cloud, surface reflectance etc. OC scaled linearly to SO4. SO4 from Restad et al. (1998).
Biomass burning (BC+OC)	Hobbs et al. (1997)	Optical parameters of biomass smoke	-0.3	3.7	-80	Uses simplified expression from Chylek and Wong (1995). Neglects radiative forcing from cloudy areas. Other parameters including estimated column burden from Penner et al. (1992).
	Iacobellis et al. (1999)	Optical parameters of biomass smoke	-0.74	3.5	-210	Three-dimensional chemical transport model and GCM. Simplified expressions also examined.
	Penner et al. (1998b) and Grant et al. (1999)	Internal/external mixture of OC and BC	-0.14 to -0.23	1.76	-80 to -120	Three-dimensional chemical transport model and GCM using biomass optical parameters modelled from two observational studies.
Fossil fuel and biomass burning BC	Haywood and Ramaswamy (1998)	External mixture	+0.4	0.27	1500	Three-dimensional GCM study using Cooke and Wilson (1996) BC data scaled to Liousse et al. (1996) total BC mass.
	Hansen et al. (1998)	Observed single scattering albedo	+0.27	NA	NA	Adjustment of modelled single scattering albedo from 1.0 to 0.92-0.95 to account for the absorption properties of BC.
	Jacobson (2001)	Internal with BC core.	+0.54	0.45	1200	GCM study using data from Cooke and Wilson (1996) scaled by a factor of 0.85.
Fossil fuel and biomass burning OC	Hansen et al. (1998)	External mixture	-0.41	NA	NA	Three-dimensional GCM study using Liousse et al. (1996) OC data. OC modelled as scattering.
	Jacobson (2001)	Internal with BC core.	-0.04 to -0.06	1.8	-17	OC treated as shell with BC core. Strongest forcing for non-absorbing OC.

Penner et al. (1998b) and Grant et al. (1999) used a chemical transport model in conjunction with a GCM to estimate a global column burden of BC from fossil fuel emissions of 0.16 mgm^-2 and a radiative forcing of +0.20 Wm^-2 for an external mixture. Cooke et al. (1999) estimated the global burden of optically active BC aerosol from fossil fuel burning from a 1° by 1° inventory of emissions to be 0.14 mgm^-2 (note the good agreement with the assumed column burdens of Haywood et al. (1997a) and Myhre et al. (1998c)) and a subsequent radiative forcing of +0.17 Wm^-2. Haywood and Ramaswamy (1998) estimated the BC radiative forcing due to fossil fuel and biomass burning to be approximately +0.4 Wm^-2 (see also Section 6.7.5), approximately half of which (+0.2 Wm^-2) is due to fossil fuel sources. Jacobson (2000, 2001) modelled BC from both fossil fuels and biomass burning sources and investigated the effects of different mixing schemes, finding a direct radiative forcing of +0.54 Wm^-2 and a normalised direct radiative forcing of 1,200 Wg^-1 when BC was modelled as an absorbing spherical core. These studies suggest that the global mean radiative forcing due to fossil fuel BC is strongest in June/July/August owing to the larger insolation coupled with higher atmospheric concentrations in the Northern Hemisphere. From these studies the normalised radiative forcing for an external mixture of BC aerosol appears better defined than for sulphate aerosol ranging from +1,123 Wg^-1 to +1,525 Wg^-1. However, all these studies used the same size distribution and exclude effects of relative humidity, thus the modelled specific extinction is independent of the relative humidity at approximately 10 m²g^-1 at 0.55 µm. Observational studies show a wide range of specific extinction coefficients, a_sp, (see Section 5.1.2 and Table 5.1) of approximately 5 to 20 m²g^-1 at 0.55 µm, thus the uncertainty in the associated radiative forcing is likely to be higher than the global model results suggest. Additionally, if BC were modelled as an internal mixture, Haywood et al. (1997a) and Myhre et al. (1998c) suggest the degree of absorption may be considerably enhanced, the radiative forcing being estimated as +0.36 Wm^-2 and +0.44 Wm^-2, respectively. Both of these studies use relatively simple effective medium mixing rules for determining the composite refractive index of internally mixed BC with sulphate and water which may overestimate the degree of absorption (e.g., Jacobson, 2000). Detailed scattering studies including a randomly positioned black carbon sphere in a scattering droplet show that the absorption is relatively well represented by effective medium approximations (Chylek et al., 1996b). Column studies by Haywood and Shine (1997) and Liao and Seinfeld (1998) and the global studies by Haywood and Ramaswamy (1998) and Penner et al. (1998b) suggest that the radiative forcing due to BC will be enhanced if BC exists within or above the cloud, but reduced if the BC is below the cloud; thus the vertical profile of BC aerosol must be determined from observations and modelled accurately.

On the basis of the calculations summarised above, the estimate of the global mean radiative forcing for BC aerosols from fossil fuels is revised to +0.2 Wm^-2 (from +0.1 Wm^-2) with a range +0.1 to +0.4 Wm^-2. The significant contribution to the global annual mean radiative forcing from cloudy regions is the main reason for the increase in the radiative forcing since the SAR. Uncertainties in determining the radiative forcing lie in modelling the mixing of BC with hygroscopic aerosols and the subsequent wet deposition processes which consequently influence the modelled atmospheric lifetime and burden of BC aerosol. Additionally, mixing of BC with other aerosol types and cloud droplets influences the optical parameters.

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