When a dynamical system admits both fast and slow timescale
dynamics, a simplified model can be constructed by systematically
filtering out the fast dynamics. In the context of
atmospheric
dynamics, these models are called balance models, with the
quasi-geostrophic (QG) model being the most notable example. Not only is
the QG model used widely for advancing our theoretical understanding of
atmospheric and oceanic dynamics, it is also crucial for practical
applications such as model initialization and data assimilation
.
The reason is that since large scale dynamics are mostly balanced (i.e.
devoid of fast motions), using unfiltered observations in numerical
models can impart an unrealistically large component of fast motion due
to observational errors. These errors can be reduced with the aid of
balance models.

Although
the QG model is immensely useful for the midlatitudes, it is not
applicable to the tropics as a singularity develops. Previous attempts
at deriving equatorial balance models have been unsuccessful as it
filters out Kelvin waves, which play a dominate role in equatorial
dynamics.
In
this talk I will give an introduction to balance models with the aid of
a simple dynamical system. This will be followed with a discussion on
how a modified asymptotic approach can be used to systematically derive
equatorial balance models in the planetary scale regime, which captures
slow Rossby and Kelvin wave modes while filtering out fast gravity wave
motions.