This is the second in a series of posts on the effects of cloud droplet spectral dispersion. Today we’ll look at a 2000 paper by Liu and Daum in Geophysical Research Letters, Spectral dispersion of cloud droplet size distributions and the parameterization of cloud droplet effective radius.

Abstract: Parameterization of effective radius (r_e) as proportional to the cube root of the ratio of cloud liquid water content (L) to droplet concentration (N), i.e., r_e=α(L/N)1/3, is becoming widely accepted. The principal distinction between different parameterization schemes lies in the specification of the prefactor α. This work focuses on the dependence of α on the spectral dispersion of the cloud droplet size distribution. Relationships by Pontikis and Hicks [1992] and by Liu and Hallet [1997] that account for the dependence of α on the spectral dispersion are compared to each other and to cloud microphysical data collected during two recent field studies. The expression of Liu and Hallet describes the spectral dependence of α (or r_e) more accurately than the Pontikis and Hicks relation over the observed range of spectral dispersions. The comparison shows that the different treatments of α as a function of spectral dispersion alone can result in substantial differences in r_e estimated from different parameterization schemes, suggesting that accurately representing re in climate models requires predicting α in addition to L and N.

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In the next couple days, I’ll be summarizing / reviewing a few papers that deal with spectral dispersion and its effects on climate - mostly through the first indirect effect (Twomey 1977). I believe a brief explaination of the Twomey effect is in order. In order for water vapor in the atmosphere to condense, it needs to a small particle onto which it condenses. These particles are called cloud condensation nuclei (CCN). In the maritime regime, cloud formation is CCN limited - the number of cloud droplets is controlled by the number of CCN. Over continents, the air is generally filled with lots of dust and pollution that acts as CCN; it is thus limited in other ways, such as water content or dynamically limited.

In the pristine cloud stratocumulus cloud decks off the coasts of continents, we have a great large-scale experimental setup. These clouds, as described above, are CCN limited. If there were more CCN available, the number concentration of cloud droplets would increase. What effect would that have on the cloud? Twomey actually solved this way back in the 1970s. The ratio of the volume of the droplets to the area of the droplets will decrease if the amount of liquid water in the clouds stays constant. This means there will be more droplets of smaller diameter. In total, the droplets project a larger effective area for incoming solar radiation. Since liquid water does not absorb hardly any visible radiation these clouds with more, but smaller, droplets reflects a greater percentage of the incoming radiation than their non-polluted neighbors. This can be seen in so-called “ship tracks”.

Ship tracks are caused by the byproducts of combustion from large ocean-going ships. These tiny particles become additional CCN for the water vapor molecules to condense. Thus, areas where these ships passed appear brighter.

The first paper that I’ll look at in this series is by Peng and Lohmann in Geophysical Research Letters, Sensitivity study of the spectral dispersion of the cloud droplet size distribution on the indirect aerosol effect.

Abstract: To study the influence of anthropogenic aerosols on the shape of the cloud droplet size spectra (dispersion effect), we analyze observed liquid water cloud data during two Canadian field studies. Scaled by the parameter β, which is a function of the relative dispersion of cloud droplet spectra, the calculated cloud albedo shows better agreement with the independently measured cloud albedo than the cloud albedo calculated without scaling. The scaling factor β is positively correlated with the cloud droplet number concentration. A linear relationship between β and the cloud droplet number concentration obtained from different field studies is applied to the ECHAM4 general circulation model. The global mean indirect aerosol effect at the top of atmosphere including the dispersion effect is reduced by 0.2 W m−2 as compared to the reference simulation. This accounts for about 1/3 of the reduction that needed to be imposed on the simulated anthropogenic indirect aerosol effect by Lohmann and Lesins [2002] .

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