Gibbs states and Brownian models for coexisting haze and cloud droplets
Abstract: Cloud microphysics studies include how tiny cloud droplets grow, and become rain. This is crucial for understanding cloud properties like size, lifespan, 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. K\"ohler's theory explains initial droplet growth but struggles with large particle groups. Here, we present a stochastic, analytical framework building on K\"ohler's theory to account for (monodisperse) aerosols and cloud droplets 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 lab experiments, offering a new perspective on haze-to-cloud transition and small cloud formation.
- L. Bengtsson, Environmental Research Letters 5, 025202 (2010).
- T. Várnai and A. Marshak, Geophysical Research Letters 36 (2009).
- A. P. Khain and M. Pinsky, Physical Processes in Clouds and Cloud Modeling (Cambridge University Press, 2018).
- H. Köhler, Trans. Faraday Soc. 32, 1152 (1936).
- A. V. Korolev and I. P. Mazin, J.Atmos.Sci. 60, 2957 (2003).
- S. Arabas and S. Shima, Nonlinear Processes in Geophysics 24, 535 (2017).
- Y. A. Kuznetsov, Elements of Applied Bifurcation Theory (Springer, 2004).
- R. Shaw, Annual Review of Fluid Mechanics 35, 183 (2003).
- W. W. Grabowski and G. C. Abade, Journal of the Atmospheric Sciences 74, 1485 (2017).
- J. M. Wallace and P. V. Hobbs, Atmospheric Science, an Introductory Survey (Elsevier, 2006).
- N. Berglund, (2011), 10.48550/ARXIV.1106.5799.
- G. A. Pavliotis, Stochastic Processes, Vol. 60 (Springer, New York, 2014).
- H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer, 1989).
- R. McGraw and Y. Liu, Geophysical Research Letters 33 (2006), 10.1029/2005GL023545.
- H. Kramers, Physica 7, 284 (1940).
- B. J. Matkowsky and Z. Schuss, SIAM Journal on Applied Mathematics 40, 242 (1981).
- N. Berglund and B. Gentz, Nonlinearity 15, 605 (2002).
- P. Squires, Tellus 8, 443 (1956).
- P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Vol. 23 (Springer Berlin Heidelberg).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.