AGEOSTROPHIC FORCING IN A HEIGHT TENDENCY EQUATION : TWO CASE STUDIES

Ageostrophic motions, and ageostrophic (AG) vorticities, have been traditionally viewed as a response to dynamic and thermodynamic forcing processes, that when applied, perturb the balanced state of the atmosphere. These motions have typically been analyzed in the context of an atmosphere that is initially in geostrophic balance. AG motions or AG winds have been considered to be a component of the observed wind, or the difference between the observed wind and the geostrophic wind (e.g., Trenberth and Chen, 1988, hereafter TC88). The AG wind is proportional to and to the left (right) of the wind acceleration vector in Northern (Southern) Hemisphere (e.g., Bluestein, 1992). An atmosphere initially in geostrophic balance will respond to some imposed forcing mechanism that generates AG motions and induces vertical motions. Thus, vertical motions, and the 'secondary' circulations they are part of, are also considered an important component in examining AG circulations (e.g. Uccellini et al., 1984; Keyser et al., 1989; Loughe et al., 1995). Formulations for the AG winds have included calculating this quantity as a residual, which is dependent upon how geostrophy itself is defined (Phillips, 1963; Blackburn, 1985). Alternative formulations for AG motions relating AG circulations to geostrophy have also been used in the examination of the three-dimensional circulations associated with upper tropospheric jets streaks and fronts (TC88; Xu, 1992; Xu and Keyser, 1993; Loughe et al., 1995). For the calculation of AG vorticity tendencies in a height tendency equation, such as the Zwack-Okossi (Z-O) equation (Zwack and Okossi, 1986; Lupo et al., 1992), it would be ideal to find a relationship that yields an instantaneous estimate of the AG vorticity tendency that is a diagnostic quantity. The Z-O equation has been used as the diagnostic framework in the study of many atmospheric phenomena (e.g., Lupo et al., 1992; King et al., 1995; Lupo and Smith, 1995, hereafter LS95; Lupo and Bosart, 1999; Zhang et al., 1999). Of these papers, only Zwack and Okossi (1986) and Lupo et al. (1992) discuss the physical processes represented by the forcing terms in a detailed manner. Lupo et al. (1992) addresses the role of AG vorticity tendencies using the generalized form of the Z-O equation. They characterize this term as a “correction term that accounts for the possibility that the unbalanced atmosphere may attempt to reach a balanced state other than geostrophic”. Thus, AG vorticity tendencies, which appear explicitly in the Z-O equation, have not been __________________________________________________ *Corresponding author address: Anthony R. Lupo, Department of Soil and Atmospheric Sciences, 109 Gentry Hall, University of Missouri-Columbia, Columbia, MO 65211. E-mail: LupoA@missouri.edu. viewed solely as either a forcing mechanism or a response to unbalanced forcing in a strict sense within this framework. Therefore, the exact role of AG vorticities in this equation has not been satisfactorily addressed. An expression is developed here that can be substituted for the AG vorticity tendency in the Z-O equation. This relationship is derived using the TC88 methodology, which describes the AG wind. In deriving this relationship, it will be shown that the AG vorticity tendency term in the Z-O equation can be interpreted in the traditional sense and as a forcing mechanism. Also, it will be shown that the AG vorticity tendency can be partially partitioned among the other terms in the Z-O equation. Finally, it will be shown that the derived relationship produces a better estimate of the total ZO height tendencies than simply calculating the AG vorticity tendency in the equation as a residual.