tokens: distribution is the same as for the monodispere case. For the broad distribution between 10 −8 and 10 −4 bar, the single-scattering albedo of the Gaussian distribution () is always higher than that of the monodisperse case (), see the right two plots of Fig. 5 . The increase for the initial broadening around 10 −7 bar is wavelength independentand peaks at ( Fig. 5 , bottom right). The second peak in the increase of the albedo from the monodispserse case occurs at about 10 −5 bar, and this time is wavelength dependent with a significantly lower increase of only a factor of 2 for λ = 0.1 μ m, as opposed to increases by a factor greater than 4 for all longer wavelengths. This is because in this region and the fraction of cloud particles in the Rayleigh scattering regime ( Q sca ∝ λ −4 ) varies for each wavelength for a broad size distribution. Although an increase of half an order of magnitude in albedo seems substantial when the total extinction of the atmosphere is calculated, the peak extinction is dominated by regions with high mass fractions of cloud particles ( ρ d ∕ ρ ). The mass fraction of cloud particles peaks around the millibar level in the atmosphere, which does not significantly overlap with regions of high nucleation rates ( Fig. 5 , bottom left) where the local size distribution is broad. The size distribution therefore has little effect on properties such as optical depth ( Fig. 9 ). Wakeford Sing (2015) also found that for a log-normal distribution, the cumulative effect of transmission spectra of clouds is dominated by larger particles in the distribution. An asymmetric distribution, such as the log-normal distribution, has a greater number of large particles than the Gaussian distribution considered here, and may produce greater deviations from the monodisperse case. It has been found recently to have an effect on retrieved cloud particle size ( Benneke et al. 2019a ). We note, however, that none of the size distributions used in retrieval approaches are based on a consistent cloud model, and therefore no conclusion can be drawn about the shape of the particle size distribution from such retrieval approaches. 5 Optical effects of non-spherical particles To determine the effect of non-spherical cloud particles, we return to the T eff = 1800 K, log ( g ) = 3.0 atmosphere with compact monodisperse cloud particles. When a distribution of hollow spheres is used, as described in Sect. 2.5 , the albedo generally decreases compared to the compact monodisperse case ( Fig. 6 , top right). This is due to the high f hol end of the hollow sphere distribution, where the cloud particles have a large surface area (which is not conserved across the distribution of hollow spheres) and thus increase absorption ( Min et al. 2003 ). Furthermore, Fig. 9 shows that for the compact case (red line), the inclusion of non-spherical particles leads to an increase in optical depth in the silicate features between 10− 20 μ m. This result is in good
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