Cloud microphysics studies include how tiny cloud droplets grow and become rain. This is crucial for understanding cloud properties like size, life span, and impact on climate through radiative effects. Small weak-updraft clouds near the haze-to-cloud transition are especially difficult to measure and understand. They are abundant but hard to capture by satellites. Köhler’s theory explains initial droplet growth but struggles with large particle groups. Here, we present a stochastic, analytical framework building on Köhler’s theory to account for (monodisperse) aerosols and cloud droplet interaction through competitive growth in a limited water vapor field. These interactions are modeled by sink terms, while fluctuations in supersaturation affecting droplet growth are modeled by nonlinear white noise terms. Our results identify hysteresis mechanisms in the droplet activation and deactivation processes. Our approach allows for multimodal cloud’s droplet size distributions supported by laboratory experiments, offering a different perspective on haze-to-cloud transition and small cloud formation.

中文翻译：

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共存的雾霾和云滴的吉布斯态和布朗模型


云微物理学研究包括微小的云滴如何生长并变成雨。这对于了解云的大小、寿命和通过辐射效应对气候的影响等特性至关重要。靠近霾到云过渡的小型弱上升气流云特别难以测量和理解。它们数量丰富，但很难被卫星捕获。Köhler 的理论解释了最初的液滴生长，但很难处理大颗粒群。在这里，我们提出了一个基于 Köhler 理论的随机分析框架，以解释（单分散）气溶胶和云滴在有限水蒸气场中通过竞争性增长的相互作用。这些交互作用由汇项建模，而影响液滴生长的过饱和度波动由非线性白噪声项建模。我们的结果确定了液滴活化和失活过程中的滞后机制。我们的方法允许由实验室实验支持的多模态云的液滴大小分布，为雾霾到云的转变和小云的形成提供了不同的视角。