His major contribution was the primitive equations which are used in climate models.

Robert, A., 1983: The design of efficient time integration schemes for the primitive equations.

With this approximation, the primitive equations become the following:

In order to fully linearize the primitive equations, one must assume the following solution:

This analytic solution is only possible when the primitive equations are linearized and simplified.

Upon linearization, the primitive equations yield the following dispersion relation:

Within any modern model is a set of equations, known as the primitive equations, used to predict the future state of the atmosphere.

The (linearised) primitive equations then become the following:

Smagorinsky, J., 1960: General circulation experiments with the primitive equations as a function of the parameters.

For example, the primitive equations which weather forecast models solve are more easily expressed in terms of geopotential than geometric height.

Smagorinsky published a seminal paper in 1963 on his research using primitive equations of atmospheric dynamics to simulate the atmosphere's circulation.

Collaborative Research and Training Site, Review of the Primitive Equations.

Commonly, the set of equations used to predict the known as the physics and dynamics of the atmosphere are called primitive equations.

With the exception of the second law of thermodynamics, these equations form the basis of the primitive equations used in present-day weather models.

In general, nearly all forms of the primitive equations relate the five variables u, v, ω, T, W, and their evolution over space and time.

Smagorinsky, J., 1963: General Circulation experiments with the primitive equations I. The basic experiment.

Kwizak, M. and A. Robert, 1971: A semi-implicit scheme for grid point atmospheric models of the primitive equations.

They are used with Coriolis forces in atmospheric and oceanic modeling, as a simplification of the primitive equations of atmospheric flow.

Smagorinsky, J., 1958: On the numerical integration of the primitive equations of motion for baroclinic flow in a closed region.

The primitive equations lead to the linearized equations for perturbations (primed variables) in a spherical isothermal atmosphere:

The operational GEM model dynamics is formulated in terms of the hydrostatic primitive equations with a terrain following pressure vertical coordinate (h).

You spoke of the primitive equations of gravitation and say it is primitive because its discovery is lost in the mists of antiquity.

The precise form of the primitive equations depends on the vertical coordinate system chosen, such as pressure coordinates, log pressure coordinates, or sigma coordinates.

Between 1963 and 1970, Robert developed the semi-implicit time integration algorithm for an efficient integration of the primitive equations for numerical weather prediction and climate models.

The primitive equations are a set of nonlinear differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models.