Impact of Dust Radiative Forcing upon Climate - Mineral Dust: A Key Player in the Earth System - page 330

The surface forcing has limited influence upon the equilibrium air temperature
because this forcing is balanced by surface radiative and turbulent fluxes that depend
upon the contrast in temperature and moisture between the lower boundary and
the air just above. Consequently, the surface forcing by itself is not sufficient
to simultaneously constrain the temperature of both the lower boundary and the
overlying air. An additional constraint is needed, relating the climate perturbation
to any energy imbalance at TOA or the lateral boundary of the dust layer. This
makes the climate perturbation by aerosols after the return to equilibrium more
difficult to anticipate than the initial response because the final perturbation is not
determined solely by the local forcing, but by a convolution of the forcing over
the entire extent of the perturbed circulation. Regional adjustment occurs over the
Rossby radius of deformation, which is inversely related to the Coriolis parameter.
This distance of adjustment is especially large in the Tropics, as demonstrated by the
observed tropic-wide response to warming of the eastern equatorial Pacific Ocean
during El Niño events (Yulaeva and Wallace 1994 ). This suggests by analogy that the
entire Tropics adjust in concert to dust radiative forcing, even if the largest aerosol
concentration is restricted to the vicinity of the arid source regions. Temperature
adjustment far beyond the regional extent of aerosol forcing has been demonstrated
in a number of models (Shindell et al. 2010 ).
The equilibrium surface temperature is controlled primarily by the TOA forcing
if two conditions are satisfied. First, the lower troposphere must be sufficiently
humid and opaque to thermal wavelengths that most OLR originates in the upper
troposphere. Then, the TOA forcing F T is compensated by an OLR anomaly ıOLR
that is related to an anomaly of the upper tropospheric emitting temperature ıT E
according to

a R 4T E ıT E ; a F F T D a R ıOLR D (13.1)

where is the Stefan-Boltzmann constant and T E is the unperturbed emitting
temperature. Here, a F and a R refer to the areal extent of the forcing and response,
respectively. As noted above, aerosol forcing is usually restricted to an area
downwind of its source that is small compared to the extent of the response.
The second condition is that the column must be efficiently mixed by deep
convection so that the temperatures of the upper troposphere and surface are coupled
by a moist adiabat. Then

ıh E ; ıh S D (13.2)

where h Lq is the moist static energy that is constant along a

moist adiabat; ıh S and ıh E are the anomalous moist static energy at the surface
and saturated value at the emitting level, respectively. (C p is the specific heat of air,
g is gravity, z is height, L is the latent heat of vaporization, and q is the specific
humidity.) If the height of the emitting level is unperturbed by dust, then ıh E D
C P ıT E , neglecting changes in upper tropospheric moisture. In addition, ıh S

D C P T C g z C

D

C P ıT S C Lıq S ,whereıT S and ıq S are the anomalous surface air temperature and