Previous research on the direct effect of atmospheric aerosols on clim
ate has estimated the average radiative forcing per unit sulfate mass,
and has used this average to calculate the magnitude and spatial dist
ribution of sulfate forcing. In this paper, we posit that radiative fo
rcing is often a nonlinear function of sulfate mass concentration. In
contrast to measures of average forcing, we introduce the concept of '
'marginal forcing'', which is defined as the change in radiative forci
ng for an incremental change in sulfate concentration. A multi-compone
nt, size-resolved aerosol box model is used, which couples an aerosol
chemical equilibrium model with a model for calculating radiative forc
ing based on Mie theory. The results for a typical nonurban continenta
l aerosol show that total aerosol mass and radiative forcing are nonli
near functions of sulfate concentration. This nonlinearity is mainly d
ue to the chemical interaction of sulfate with volatile inorganic comp
onents of the aerosol (ammonium, nitrate, and water). As a result, the
marginal forcing varies significantly as a function of sulfate concen
tration, from - 550 to + 20 W (g SO42-)(-1) at a relative humidity (RH
) of 80%. Estimates of marginal forcing are strongly sensitive to RH.
Absolute marginal forcing also decreases significantly with total nitr
ate concentration, increases with total ammonia concentration, and gen
erally increases with temperature. We estimate hat the bias in assumin
g a constant average forcing may cause overestimates in local continen
tal aerosol radiative forcing by up to 50%, and in the marginal forcin
g by a factor of two or more.This bias is greatest at intermediate sul
fate concentration, high RH, high total nitrate concentration,low tota
l ammonia concentration( greater than or equal to 2 mu g m(-3)), and l
ow temperature. (C) 1998 Published by Elsevier Science Ltd. All rights
reserved.