When a dynamical system admits both fast and slow timescale dynamics, a simplified model can be obtained by filtering out the fast dynamics systematically. In the context of atmospheric dynamics, these models are called balance models, with the quasi-geospherc (QG) model being the most famous example. As synoptic and planetary scale atmospheric dynamics are observed to be dominated by slow Rossby wave dynamics, observations used for initializing numerical models must be filtered accordingly using balance models, or else the error in the initial data will impart a spurious component of fast inertia-gravity wave motion to the solution.

In this talk I will first explore a simple chemical system with fast and slow dynamics, and derive the corresponding balance model. This simple example is used to highlight some of the key features of general balance models. I will then proceed to show how a similar argument can be applied to a shallow water model for the atmosphere to derive the QG model, and provide some applications to show why balance models are important. If time permits I'll illustrate how asymptotic expansion can be used to systematically develop higher order balance models. Finally I will explain how a lack of proper balance model near the equator affects data assimilation and reanalysis products.