Until recently, general circulation models (GCMs) of the atmosphere were unable to simulate the quasi-biennial oscillation (QBO) in the zonal mean wind which is observed in the equatorial stratosphere. It is well-known that the QBO is driven by the deposition of momentum by waves propagating upwards from the troposphere. However, there has been considerable debate as to the relative contributions of the different types of waves involved: planetary-scale Kelvin and Rossby-gravity waves, and small-scale gravity waves. It is now understood that gravity waves play an important role in driving the QBO and that their effects must be accounted for in GCMs by means of parameterizations. In the past few years, GCMs that include parameterized gravity wave drag have had some success in generating QBOs. However, the characteristics of the simulated QBOs are, in general, different for each model. This would suggest that there is a need for an understanding of the properties of the different parameterization schemes, the mechanisms by which they generate QBOs and the conditions under which they are able to do so.

In this study, we examine several well-known gravity wave drag schemes using simple models of the QBO: a one-dimensional zonal-mean model and a two-dimensional balance model that includes a seasonal cycle and the upwelling of the tropical Hadley circulation. The effects of the gravity waves are studied in isolation, as well as in combination with equatorial planetary waves, which are also represented by a parameterization scheme. We have determined the constraints that are needed for each scheme - or combination of schemes - to be able to generate a QBO with the one-dimensional model. These include restrictions on the various parameters, on the initial configuration and on the gravity wave source spectrum. Ultimately the plan is extend these constraints to provide some guidance for the use of parameterization schemes in GCMs. As a step towards that, we have generalized them for application in the two-dimensional model.