Estimation of cloud condensation nuclei concentration from aerosol optical quantities: influential factors and uncertainties

Large-scale measurements of cloud condensation nuclei (CCN) are difficult to obtain on a routine basis, whereas aerosol optical quantities are more readily available. This study investigates the relationship between CCN and aerosol optical quantities for some distinct aerosol types using extensive observational data collected at multiple Atmospheric Radiation Measurement (ARM) Climate Research Facility (CRF) sites around the world. The influences of relative humidity (RH), aerosol hygroscopicity (<i>f</i>_RH) and single scattering albedo (SSA) on the relationship are analyzed. Better relationships are found between aerosol optical depth (AOD) and CCN at the Southern Great Plains (US), Ganges Valley (India) and Black Forest sites (Germany) than those at the Graciosa Island (the Azores) and Niamey (Niger) sites, where sea salt and dust aerosols dominate, respectively. In general, the correlation between AOD and CCN decreases as the wavelength of the AOD measurement increases, suggesting that AOD at a shorter wavelength is a better proxy for CCN. The correlation is significantly improved if aerosol index (AI) is used together with AOD. The highest correlation exists between CCN and aerosol scattering coefficients (&sigma;_sp) and scattering AI measured in situ. The CCN–AOD (AI) relationship deteriorates with increasing RH. If RH exceeds 75%, the relationship where AOD is used as a proxy for CCN becomes invalid, whereas a tight &sigma;_sp–CCN relationship exists for dry particles. Aerosol hygroscopicity has a weak impact on the &sigma;_sp–CCN relationship. Particles with low SSA are generally associated with higher CCN concentrations, suggesting that SSA affects the relationship between CCN concentration and aerosol optical quantities. It may thus be used as a constraint to reduce uncertainties in the relationship. A significant increase in &sigma;_sp and decrease in CCN with increasing SSA is observed, leading to a significant decrease in their ratio (CCN / &sigma;_sp) with increasing SSA. Parameterized relationships are developed for estimating CCN, which account for RH, particle size, and SSA

CLT-groups with Hall S-quasinormally embedded subgroups

A subgroup H of a finite group G is said to be Hall S-quasinormally embedded in G if H is a Hall subgroup of the S-quasinormal closure H SQG . We study finite groups G containing a Hall S-quasinormally embedded subgroup of index p n for each prime power divisor p n of the order of G.Підгрупа H скінченної групи G називається підгрупою Холла, S-квазінормально вкладеною в G, якщо H — підгрупа Холла S-квазінормального замикання HSQG. Вивчаються скінченні групи G, що містять S-квазінормально вкладені підгрупи Холла індексу pn для кожного простого степеневого дільника pn порядку G