标题： 超越单一模型：适用于亚恒星大气云微物理的多分散矩方法 II. 用于 GCM 应用的三阶矩伽马分布公式 显示英文标题

标题： Beyond monoculture: Polydisperse moment methods for sub-stellar atmosphere cloud microphysics II. A three-moment gamma distribution formulation for GCM applications

摘要： 上下文。 了解云粒子大小分布的形状如何影响亚恒星大气的大气特性是一个关键研究领域，特别是在JWST时代，宽波长覆盖范围的观测对粒子大小分布敏感。因此，阐明潜在的云微物理过程如何影响大小分布，以更好地理解云如何影响观测到的大气特性是重要的。 目标。 在本文中，我们旨在将论文I中的亚恒星大气微物理云形成框架扩展为包括假设多分散伽马粒子大小分布的影响，这需要一个三阶矩解集方程。 方法。 我们开发了一个三阶矩框架，用于亚恒星矿物云粒子的微物理成核、凝结、蒸发和碰撞生长，假设采用伽马分布。 如论文I所示，我们使用一个简单的二维Y矮星KCl云形成场景来演示多分散性的影响，并将结果与单分散情况进行比较。 结果。 我们的三阶矩方案提供了一个适用于任何具有定义矩生成表达式的大小分布的通用框架。 在我们的测试案例中，我们展示了伽马分布随高度的变化，最初在云底较宽，在较低压力下变窄。 我们发现，伽马分布和单分散云结构之间的差异可能很大，这取决于大气的表面重力。 结论。 我们提出了一种自洽的框架，用于在亚恒星微物理云研究中使用矩方法包含多分散性的影响。 显示英文摘要

摘要： Context. Understanding how the shape of cloud particle size distributions affects the atmospheric properties of sub-stellar atmospheres is a key area to explore, particularly in the JWST era of broad wavelength coverage, where observations are sensitive to particle size distributions. It is therefore important to elucidate how underlying cloud microphysical processes influence the size distribution, in order to better understand how clouds affect observed atmospheric properties. Aims. In this follow-up paper, we aim to extend our sub-stellar atmosphere microphysical cloud formation framework from Paper I to include effects of assuming a polydisperse gamma particle size distribution, requiring a three-moment solution set of equations. Methods. We develop a three-moment framework for sub-stellar mineral cloud particle microphysical nucleation, condensation, evaporation and collisional growth assuming a gamma distribution. As in Paper I, we demonstrate the effects of polydispersity using a simple one-dimensional Y-dwarf KCl cloud formation scenario, and compare the results with the monodisperse case. Results. Our three-moment scheme provides a generalised framework applicable to any size distribution with a defined moment generation expression. In our test case, we show that the gamma distribution evolves with altitude, initially broad at the cloud base and narrowing at lower pressures. We find that differences between the gamma and monodisperse cloud structures can be significant, depending on the surface gravity of the atmosphere. Conclusions. We present a self-consistent framework for including the effects of polydispersity for sub-stellar microphysical cloud studies using the moment method.