![]() ![]() Previous studies have tended to view precipitation behavior primarily as a function of cloud formation and evolution. Finally, interpreting solar system geological records shaped by fluvial erosion-for example, ancient Mars' large-scale valley networks and crater modifications (e.g., Craddock & Howard, 2002), modern Titan's lakes and rivers (e.g., Lorenz et al., 2008), and Archean Earth's fossilized raindrops (Kavanagh & Goldblatt, 2015 Som et al., 2012)-requires an understanding of changes in precipitation events as planetary conditions vary.ĭespite the importance of precipitation, understanding its behavior in different planetary environments remains a major theoretical challenge (e.g., Vallis, 2020). On terrestrial planets generally, the intensity, frequency, and spatial distribution of liquid precipitation are essential in governing surface erosion via runoff and physical weathering (e.g., Margulis, 2017) as well as chemical weathering fundamental to the carbon-silicate cycle (Graham & Pierrehumbert, 2020 Macdonald et al., 2019 Walker et al., 1981). On Earth, global precipitation patterns play a critical role in determining local ecology and have significant societal impacts (Margulis, 2017). The role of precipitation in dictating radiative balance is especially important on dry planets (Abe et al., 2011) and planets in or near a runaway greenhouse state (e.g., Leconte et al., 2013 Pierrehumbert, 1995). These properties, in turn, have direct radiative implications via the greenhouse effect and albedo changes (e.g., Pachauri et al., 2014 Pierrehumbert, 2010 Pierrehumbert et al., 2007 Shields et al., 2013 Yang et al., 2014). Precipitation's role in transporting condensible mass from the atmosphere to the surface (or the deep atmosphere on gaseous planets) exerts a strong influence on the relative humidity distribution (Lutsko & Cronin, 2018 Ming & Held, 2018 Romps, 2014 Sun & Lindzen, 1993), cloud lifetimes and occurrence rates (Seeley et al., 2019 Zhao et al., 2016), and condensible surface distributions (Abe et al., 2011 Wordsworth et al., 2013). The behavior of precipitation is essential to setting planetary radiative balance. Precipitation is a transient state, but though its effects are largely indirect, they have immense consequences for planetary climate. Because precipitating particles can fall far from the air mass where they form, they redistribute both heat and the condensible species within an atmosphere. Extensive vertical displacement relative to the local air mass distinguishes precipitation from clouds. Within a planetary condensible cycle, precipitation is the transport of the condensible species in a condensed phase (liquid or solid) through the atmosphere and, for terrestrial planets, to the surface. Our results have implications for precipitation efficiency, convective storm dynamics, and rainfall rates, which are properties of interest for understanding planetary radiative balance and (in the case of terrestrial planets) rainfall-driven surface erosion. Starting from the equations governing raindrop falling and evaporation, we demonstrate that raindrop ability to vertically transport latent heat and condensible mass can be well captured by a new dimensionless number. We demonstrate that these simple, interrelated characteristics tightly bound the possible size range of raindrops in a given atmosphere, independently of poorly understood growth mechanisms. Here, we show how three properties that characterize falling raindrops-raindrop shape, terminal velocity, and evaporation rate-can be calculated as a function of raindrop size in any planetary atmosphere. The problem I'm having is understanding the solution, the first step of the model answer is: "Let the raindrop have a radius r, after falling a distance y through the cloud.The evolution of a single raindrop falling below a cloud is governed by fluid dynamics and thermodynamics fundamentally transferable to planetary atmospheres beyond modern Earth's. Assuming that the raindrop starts with negligible size and picks up any condensed water it passes through" ![]() What volume fraction of the cloud is made of condensed water. After falling 1km it has a radius of 5mm. Previous post: I've been trying to solve this physics problem today " Spherical raindrop falls through a cloud with uniform density. ![]() I don't get why it should be like that, any idea? Where $V_c$ is the volume swept by the ball and $y$ is the position of the ball along the moving direction. EDIT: I've read that a ball moving in a rectilinear motion with a non-constant radio, $r$ satisfies that ![]()
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