The representation of clouds and associated processes of rain and snow formation remain one of the major uncertainties in climate and weather prediction models. In a companion paper (part I), we systematically derived a two-moment bulk cloud microphysics model for warm rain based on the kinetic coalescence equation (KCE) and the use of stochastic approximations to close the high order moment terms, independently of the collision kernel. Conservation of mass and consistency of droplet number concentration of the evolving cloud distribution combined with numerical simulations are used as design principles to reduce the parametrization problem to three key parameters. Here, we further derive physical limits or region of validity for these three parameters based on the physics of collision and coalescence processes: “the stochastic region of validity”. More importantly, in this second part, we validate the stochastically derived bulk cloud microphysics model against detailed simulations based on the KCE and in comparison with a similar model by Seifert and Beheng (J Atmos Sci 59–60:265–281, 2001; hereafter SB01) who instead prescribed the shapes of the droplet distributions of rain and clouds in order to close the high-order moments and have done so specifically for one given kernel only. A thorough parameter exploration of the stochastic validity region is conducted, and parameter values that faithfully reproduce the detailed KCE results are identified. The results show that for typical parameter values, dependent on the environmental conditions, the new parameterization outperforms that of SB01 when compared to the KCE benchmark simulations. These results can be explored in the future to design a Markov jump process to randomly select adequate parameters within the validity region conditional on the environmental conditions and the age of the cloud. Furthermore, sensitivity tests indicate that the stochastically derived model can be used with a time step as large as 30 s without significantly compromising accuracy, which makes it very attractive to use in medium to long range weather prediction models.

云的表示以及雨雪形成的相关过程仍然是气候和天气预报模型中的主要不确定因素之一。在随附的论文（第一部分）中，我们基于动力学合并方程（KCE）并使用随机逼近来独立于碰撞而封闭高阶矩项，系统地得出了暖雨的两步体云微物理模型。核心。设计原理是将进化云分布的质量守恒和液滴数目浓度的一致性与数值模拟相结合，作为将参数化问题简化为三个关键参数的设计原则。在这里，我们根据碰撞和合并过程的物理原理，进一步得出这三个参数的物理极限或有效范围：“有效随机范围”。更重要的是，在第二部分中，我们对照基于KCE的详细模拟，并与Seifert和Beheng的类似模型进行比较，验证了随机导出的体云微物理模型（J Atmos Sci 59-60：265-281，2001；此后） SB01）而是规定了雨和云的液滴分布的形状，以便封闭高阶矩，并且只针对一个给定的内核执行了此操作。对随机有效性区域进行了彻底的参数探索，并确定了忠实再现详细KCE结果的参数值。结果表明，与典型的参数值（取决于环境条件）相比，与KCE基准仿真相比，新的参数化性能优于SB01。将来可以探索这些结果，以设计马尔可夫跳跃过程，以根据环境条件和云龄确定在有效区域内随机选择适当的参数。此外，敏感性测试表明，随机衍生模型可以在不影响准确性的情况下以30 s的时间步长使用，这使其在中长期天气预报模型中的使用非常有吸引力。