Modeling of the atmosphere and ocean without the "traditional approximation"

The dynamical equations used in the current general circulation models of the atmosphere and ocean (GCMs) adopt two major simplifications -- “shallowness” and “traditional” approximations. The next–generation GCMs likely discard these restrictions. Since removing these approximations requires substantial model changes, it is desirable to evaluate the worth of removing these simplifications. This talk will focus on understanding the nature of the “traditional approximation (TA)” that neglects the Coriolis terms proportional to the cosine of the latitude.

I will first give a historical review on the justification of the TA which has been rather contentious as Phillips wrote in 1966 as “a long-standing point of confusion”. The role of cos(latitude) Coriolis parameter, F, in addition to sin(latitude) Coriolis parameter, f, has been investigated occasionally in the past, but the efforts were rather spotty and the literature has been obscure. A renewed interest in questioning the wisdom of the TA has revived in the last ten years or so due to an effort to improve the fidelity of the GCMs.

I will then summarize the recent findings on the role of F. There is a technical difficulty in analyzing the dynamical systems on sphere including F, but obtaining analytical solutions is possible in some special cases of Cartesian coordinates on the tangent and beta-planes at mid-latitudes and the equator. Without the TA, the axis of rotation is not parallel with the gravity, except at the poles. This fact together with the influence of vertical boundary creates unfamiliar inertio-gravity modes in addition to the traditional ones. In other words, the traditional inertio-gravity waves are incomplete by not having the role of F. The deficiency of not including the complete Coriolis effects in the model becomes more acute in the tropics where the influence of f other than the beta-effect becomes very small.

As the models of the atmosphere and ocean have progressed from the quasi-geostrophic to primitive- equation formulations, it is clear that without the role of F, the accuracy of inertio-gravity motions is compromised in the traditional GCMs.