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The impacts of aerosol loading on surface precipitation from mid-latitude deep convective systems are examined using a bin microphysics model. For this, a precipitation case over north central Mongolia, which is a high-altitude inland region, on 21 August 2014 is simulated with aerosol number concentrations of 150, 300, 600, 1200, 2400, and 4800 cm−3. The surface precipitation amount slightly decreases with increasing aerosol number concentration in the range of 150–600 cm−3, while it notably increases in the range of 600–4800 cm−3 (22% increase with eightfold aerosol loading). We attempt to explain why the surface precipitation amount increases with increasing aerosol number concentration in the range of 600–4800 cm−3. A higher aerosol number concentration results in more drops of small sizes. More drops of small sizes grow through condensation while being transported upward and some of them freeze, thus increasing the mass content of ice crystals. The increased ice crystal mass content leads to an increase in the mass content of small-sized snow particles largely through deposition, and the increased mass content of small-sized snow particles leads to an increase in the mass content of large-sized snow particles largely through riming. In addition, more drops of small sizes increase the mass content of supercooled drops, which also leads to an increase in the mass content of large-sized snow particles through riming. The increased mass content of large-sized snow particles resulting from these pathways contributes to a larger surface precipitation amount through melting and collision-coalescence.

In this paper, we derive high-order Lorenz–Stenflo equations with 6 variables and investigate periodic behaviors as well as stability of the equations. The stability of the high-order Lorenz–Stenflo equations is investigated by the linear stability analysis for various parameters. A periodicity diagram is also computed and it shows that the high-order Lorenz–Stenflo equations exhibit very different behaviors from the original Lorenz–Stenflo equations for both periodic and chaotic solutions. For example, period 3 regime for large parameters and scattered periodic regime are newly observed, and chaotic regimes exist for smaller values of r but for larger values of s than the original equations. In contrast, similarities such as the enclosure of the chaotic regime by the periodic regime or complex periodic regimes inside the chaotic regime are also observed for both the original and high-order Lorenz–Stenflo equations.

In this paper, we investigate periodic behaviors of the Lorenz–Stenflo equations in wide ranges of parameters. Regimes of periodic solutions and chaotic solutions are computed and distinguished by local maximum values of a dynamic variable Z. Complex behaviors of the periodic solutions are observed inside a regime of the chaotic solutions which is closed and surrounded by a regime of the periodic solutions where a feature of disconnected bifurcations is observed. It is found that not only a regime of fixed solutions but also regimes of solutions with period 1 and 2 remain for sufficiently large parameters.