Balance Model in a Conditionally Unstable Tropical Atmosphere

Abstract

A scale analysis of large-scale tropical disturbances in a conditionally unstable atmosphere is made by using a Mercator map projection at the equator. The release of latent heat in convection is included through the CISK process. Provided the north-south scale of the disturbances considered is of the order of 1000 km, we obtain a balance system in which the balance equation is used to estimate the geopotential height as a function of the prescribed streamfunction, and the equation of potential vorticity includes the condensation effect. This balance system is valid not only in tropical but also extratropical regions and, if there is no condensation, becomes identically equal to the system obtained by Charney. The problem of finding the instability of large-scale tropical disturbances is treated by using a three-level linearized balance system applied over a region extending from the equator to 30N. The frequency equation is solved numerically to find unstable waves. It appears that the balance system is capable of simulating many of the observed structural features of tropical disturbances with a remarkable degree of reality. When the basic zonal flow is set to zero we obtain a type of unstable wave, which, by being prominent in the upper troposphere with a period of about 4 days and a zonal wavelength of approximately 10,000 km, is similar to the Yanai-Maruyama wave. In the case of an easterly zonal current with westerly vertical shear, some unstable waves greatly resemble, in their structural features, the lower tropospheric equatorial waves observed in the easterly trade wind regime. Their wavelength range is 3000?6000 km and that of their period 3?5 days; their maximum wind amplitude is located either at the equator or in the vicinity of 10N. When the observed wind is assigned as the basic zonal flow, some tropical disturbances with wavelengths of 5000 km and periods of 20?27 days become unstable by receiving most of their kinetic energy from the zonal current.