Influence of mixing on evaluation of the aerosol first indirect effect
Hongfei Shao and Guosheng Liu

Abstract: The aerosol first indirect effect is known to cool the Earth radiatively. However, its magnitude is very uncertain. One of the difficulties in deriving this effect is caused by the coherent variation between aerosol abundance and meteorological conditions. In this study, we demonstrate that evaluation of the aerosol first indirect effect based on comparisons of clouds with different aerosol concentrations suffers an influence of the different degrees of mixing between clean and polluted clouds. By introducing a new method capable to remove this influence, we show that the strength of the aerosol first indirect effect is about half of that estimated by many previous investigators.

These has been some discrepancy about the magnitude of the aerosol first indirect effect. As defined in equation 1 of Shao and Liu [originally from Twomey, 1977], one method of determining the first indirect effect is by measuring the ratio of the change in the cloud droplet number concentration due to changes in aerosol number concentration. This is done using in situ measurements, such as from aircraft. The second way is from remote sensing from satellites. In this method, the change in effective radius due to changes in aerosol concentrations at constant liquid water path is measured. The two methods have systematic differences in the magnitude of the first indirect effect. In situ measurements show the indirect effect (as defined above), to be from 0.16-0.29 [Chuang et al. (2000), Feingold et al. (2001), Twohy et al. (2005), Kaufman et al. (1991), Conant et al. (2004), Taylor and McHaffie (1994)], while the remotely sensed indirect effect has been from 0.073-0.13 [Sekiguchi et al. (2003), Nakajima et al. (2001), Breon et al. (2002), Feingold et al. (2003), Kim et al. (2003)]

Shao and Liu argue that “the systematic discrepancy between… [the in situ and remotely sensed values for the aerosol indirect effect]… is caused primarily by the differential loss of cloud liquid water between clean and polluted clouds.”

The biggest problem with this paper is that they redefine the first aerosol indirect effect (FAIE). The FAIE is generally considered just to be the cooling effect caused by the decrease in the effective radius of the liquid water droplets caused by the increase in cloud condensation nuclei. However, Shao and Liu combine the Twomey cooling with the heating/compensating [see the spectral dispersion series] due to the change in the cloud droplet spectral shape.

The indirect effect is defined as δlnB/δlnN_a, where B=H^1/3r_e^-1 - H is cloud depth, N_a is aerosol number concentration, and r_e is effective radius. The effective radius is defined as the third moment of the cloud droplet size distribution divided by the second moment, and is another microphysical representation of the spectral shape. As said before, this definition of FAIE includes both the effects of number concentration and spectral shape.

When they calculate the FAIE using the same data as Liu and Daum (2002), they find that the indirect effect is moderated by a factor of about 50% [from Figure 1 of that paper] - 0.17, compared with 0.33 when computed using the “standard” method. I am unsure how they found the change in the cloud droplet number concentration due to changes in aerosol number concentration when the figure does not include any information about the aerosol number concentration. Assuming they obtained the aerosol number concentration data, it still does not explain the difference between the in situ and remotely sensed measurements. The Liu and Daum data was a collection of in situ data, after Shao and Liu apply their “correction”, it is still within the range of values for the in situ data - it does not explain the systematic difference between the measurements, as it claims to do.

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