## 1. Introduction

[2] Because it is conserved in frictionless adiabatic flow in a dry atmosphere, potential vorticity is one of the most important dynamic/thermodynamic parameters. It has been studied to enhance the understanding of the genesis and development of weather systems for more than 6 decades since it was first introduced by *Ertel* [1942]. However, it is not conserved when clouds develop and release latent heat. Moist potential vorticity is thus introduced by replacing potential temperature with the equivalent potential temperature, which is conserved in frictionless moist adiabatic processes. Many studies have contributed to understanding the roles of dry and moist potential vorticity in the genesis and development of weather systems [e.g., *Bennetts and Hoskins*, 1979; *Emanuel*, 1979; *Danielsen and Hipskind*, 1980; *Thorpe*, 1985; *Hoskins and Berrisford*, 1988; *Xu*, 1992; *Montgomery and Farrell*, 1993; *Cao and Cho*, 1995; *Cho and Cao*, 1998; *Gao et al.*, 2002].

[3] However, this important physical parameter cannot be applied to the analysis of the two-dimensional (2-D) simulation data. Dry/moist potential vorticity can be expressed as ( · ∇θ_{e})/ρ, where is the absolute vorticity, θ is the potential temperature in dry air and equivalent potential temperature in moist air, ρ is the air density, and ∇ is the 3-D gradient operator. For 2-D x-z flows [e.g., *Tao and Simpson*, 1993; *Wu et al.*, 1998; *Li et al.*, 1999],

and

where u and w are the zonal and vertical wind components, respectively, x and z are the zonal and vertical coordinates, respectively, and and are the unit vectors in the zonal and vertical coordinates, respectively ( = × ). Ω is the angular speed of the Earth's rotation, and ϕ is the latitude.

For 2-D, equatorial flows . This demonstrates that the 2-D flows do not contribute to the dry/moist potential vorticity. The vertical component of planetary vorticity is ignored henceforth.

[4] The new vorticity vector in the 2-D x-z frame is

where

and θ_{e} is the equivalent potential temperature, 2Ω cos ϕ is much smaller than ζ as indicated in Figure 4a and is neglected in this study. The new vector (( × ∇θ_{e})/ρ)) has zonal (*P*_{x} = (ζ/)((∂θ_{e})/∂z)) and vertical (*P*_{z} = −(ζ/)((∂θ_{e})/∂z)) components in the 2-D x-z frame. This new vector will be used to analyze 2-D tropical convection based on hourly data from a cloud-resolving simulation. It will be demonstrated that this is an important vector whose variation is closely associated with that of tropical convection. The model, forcing, and experiment are briefly described in the next section. In section 3, 2-D modeling data will be used to analyze the vorticity and equivalent potential temperature gradients, calculate( × ∇θ_{e})/ρ, derive its tendency equation, and examine the dominant processes responsible for its variation in the tropical, deep convective regime. The summary is given in section 4.