ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-Model I-Model B-Model O B-Model I-Model I-Model B-Model O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model O O O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-CelestialObject B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: model that simulates moist convection and cloud formation across various planetary conditions. Using a regional nonhydrostatic model to study moist convection is standard practice for Earth’s atmosphere, and many numerical models—named cloud-resolving models (CRMs) or large eddy simulations (LES)—have been developed accordingly (Pielke et al. 1992 ; Bryan Fritsch 2002 ; Khairoutdinov Randall 2003 ; Pressel et al. 2015 ). Similar nonhydrostatic models have been developed for Mars (Rafkin et al. 2001 ), Jupiter (Hueso Sánchez-Lavega 2001 ; Sugiyama et al. 2014 ), and Saturn (Hueso Sánchez-Lavega 2004 ), but they lack a well-documented comparison against an accepted nonlinear solution, which seems to be the first step in developing a robust numerical model. Because there are no standard tests of nonhydrostatic models for planets other than Earth, we will primarily perform simulations against standard tests for Earth-like conditions. Then, we perform an idealized simulation of the Jovian atmosphere in radiative-convective equilibrium (RCE) to study moist convection in hydrogen atmospheres. The structure of this work is organized as follows. Section 2 is devoted to the equation of motion, which includes dry air, vapors, clouds, and precipitation. Section 3 discusses the basic microphysics scheme employed in the model. Section 4 describes the numerical schemes that are designed for simulating atmospheric flows. Section 5 provides a series of benchmark tests against known solutions in the literature. Section 6 performs an idealized RCE simulation of the Jovian atmosphere. Section 7 concludes and outlines the future applications. To make the notations consistent and clear, major symbols used in this article are summarized in Appendix A for reference. 2. Equation of Motion We solve the most generic form of the equation of motion, the fully compressible Euler equations, to avoid unnecessary assumptions that are valid only for a particular type of planet. Though Euler equations can be written in many mathematically equivalent forms, they are different when discretized and implemented in a numerical model. Bryan Fritsch ( 2002 ) have compared five different ways of implementing the Euler equations, using potential temperature, equivalent potential temperature, and liquid water potential temperature. They concluded that the form of governing equations used in a numerical model has a profound effect on the simulation of a warm rising bubble. Satoh ( 2002 ) pointed out that in a model with diabatic forcing, the change in the domain integral of total energy is generally different from energy gain/loss from the boundaries if the potential temperature is used as the prognostic variable, which causes an error of the energy budget that accumulates with time. Furthermore, the expressions of potential temperature and equivalent potential temperature become complicated when the heat capacity of the atmosphere varies with temperature or when multiple condensing