A recent achievement of climate modelers in contributing to convince the public that human activities are affecting climate is well-known, but only few know that current climate models adopt the hydrostatic primitive equations which have two major dynamical simplifications, called the "shallowness" and "traditional" approximations. These approximations may produce more than few-percent errors in the dynamics. In light of our interest in finding the change in climate due to such minute effects of increasing greenhouse gases in the atmosphere, for the design of next-generation earth system model, it is desirable to eliminate these dynamical approximations. This talk will focus on understanding the nature of the traditional approximation (TA) that neglects the Coriolis terms proportional to Cosine of the latitude. I will first give a historical review on the justification of TA which has been "rather confusing" as Norman Phillips wrote in 1966. A renewed interest in questioning the wisdom of TA has revived in the last ten years or so due to an effort to improve the fidelity of the models for weather and climate. I will then summarize recent findings on the role of Cos-Coriolis terms. Without the TA, the axis of rotation is no longer parallel with the gravity, except at the poles. This reality together with the influence of vertical boundary creates little-known inertio-gravity modes in addition to the traditional ones. In other words, with the TA the accuracy of inertio-gravity motions is compromised. Lastly, I will propose a dynamical framework of future earth system model using unified radial coordinates for the atmosphere and hydrosphere with only one minor assumption that the geopotential of the earth is a sphere.